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Ye J, Zoller P. Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics. PHYSICAL REVIEW LETTERS 2024; 132:190001. [PMID: 38804927 DOI: 10.1103/physrevlett.132.190001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Indexed: 05/29/2024]
Abstract
Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.
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Affiliation(s)
- Jun Ye
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
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2
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Eckner WJ, Darkwah Oppong N, Cao A, Young AW, Milner WR, Robinson JM, Ye J, Kaufman AM. Realizing spin squeezing with Rydberg interactions in an optical clock. Nature 2023; 621:734-739. [PMID: 37648865 DOI: 10.1038/s41586-023-06360-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 06/22/2023] [Indexed: 09/01/2023]
Abstract
Neutral-atom arrays trapped in optical potentials are a powerful platform for studying quantum physics, combining precise single-particle control and detection with a range of tunable entangling interactions1-3. For example, these capabilities have been leveraged for state-of-the-art frequency metrology4,5 as well as microscopic studies of entangled many-particle states6-11. Here we combine these applications to realize spin squeezing-a widely studied operation for producing metrologically useful entanglement-in an optical atomic clock based on a programmable array of interacting optical qubits. In this demonstration of Rydberg-mediated squeezing with a neutral-atom optical clock, we generate states that have almost four decibels of metrological gain. In addition, we perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087(1) × 10-15 at one-second averaging time, which is 1.94(1) decibels below the standard quantum limit and reaches a fractional precision at the 10-17 level during a half-hour measurement. We further leverage the programmable control afforded by optical tweezer arrays to apply local phase shifts to explore spin squeezing in measurements that operate beyond the relative coherence time with the optical local oscillator. The realization of this spin-squeezing protocol in a programmable atom-array clock will enable a wide range of quantum-information-inspired techniques for optimal phase estimation and Heisenberg-limited optical atomic clocks12-16.
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Affiliation(s)
- William J Eckner
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Nelson Darkwah Oppong
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Alec Cao
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Aaron W Young
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - William R Milner
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - John M Robinson
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Jun Ye
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA
| | - Adam M Kaufman
- JILA, University of Colorado and National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado, USA.
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3
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Hines JA, Rajagopal SV, Moreau GL, Wahrman MD, Lewis NA, Marković O, Schleier-Smith M. Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles. PHYSICAL REVIEW LETTERS 2023; 131:063401. [PMID: 37625064 DOI: 10.1103/physrevlett.131.063401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2023] [Revised: 06/08/2023] [Accepted: 06/20/2023] [Indexed: 08/27/2023]
Abstract
We report on the creation of an array of spin-squeezed ensembles of cesium atoms via Rydberg dressing, a technique that offers optical control over local interactions between neutral atoms. We optimize the coherence of the interactions by a stroboscopic dressing sequence that suppresses super-Poissonian loss. We thereby prepare squeezed states of N=200 atoms with a metrological squeezing parameter ξ^{2}=0.77(9) quantifying the reduction in phase variance below the standard quantum limit. We realize metrological gain across three spatially separated ensembles in parallel, with the strength of squeezing controlled by the local intensity of the dressing light. Our method can be applied to enhance the precision of tests of fundamental physics based on arrays of atomic clocks and to enable quantum-enhanced imaging of electromagnetic fields.
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Affiliation(s)
- Jacob A Hines
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | | | - Gabriel L Moreau
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Michael D Wahrman
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Neomi A Lewis
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Ognjen Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Bai SY, An JH. Floquet Engineering to Overcome No-Go Theorem of Noisy Quantum Metrology. PHYSICAL REVIEW LETTERS 2023; 131:050801. [PMID: 37595225 DOI: 10.1103/physrevlett.131.050801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 07/17/2023] [Indexed: 08/20/2023]
Abstract
Permitting a more precise measurement to physical quantities than the classical limit by using quantum resources, quantum metrology holds a promise in developing many revolutionary technologies. However, the noise-induced decoherence forces its superiority to disappear, which is called no-go theorem of noisy quantum metrology and constrains its application. We propose a scheme to overcome the no-go theorem by Floquet engineering. It is found that, by applying a periodic driving on the atoms of the Ramsey spectroscopy, the ultimate sensitivity to measure their frequency characterized by quantum Fisher information returns to the ideal t^{2} scaling with the encoding time whenever a Floquet bound state is formed by the system consisting of each driven atom and its local noise. Combining with the optimal control, this mechanism also allows us to retrieve the ideal Heisenberg-limit scaling with the atom number N. Our result gives an efficient way to avoid the no-go theorem of noisy quantum metrology and to realize high-precision measurements.
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Affiliation(s)
- Si-Yuan Bai
- Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou Center for Theoretical Physics, and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Jun-Hong An
- Key Laboratory of Quantum Theory and Applications of MoE, Lanzhou Center for Theoretical Physics, and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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Kraus B, Dawel F, Hannig S, Kramer J, Nauk C, Schmidt PO. Phase-stabilized UV light at 267 nm through twofold second harmonic generation. OPTICS EXPRESS 2022; 30:44992-45007. [PMID: 36522911 DOI: 10.1364/oe.471450] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2022] [Accepted: 10/19/2022] [Indexed: 06/17/2023]
Abstract
Providing phase stable laser light is important to extend the interrogation time of optical clocks towards many seconds and thus achieve small statistical uncertainties. We report a laser system providing more than 50 µW phase-stabilized UV light at 267.4 nm for an aluminium ion optical clock. The light is generated by frequency-quadrupling a fibre laser at 1069.6 nm in two cascaded non-linear crystals, both in single-pass configuration. In the first stage, a 10 mm long PPLN waveguide crystal converts 1 W fundamental light to more than 0.2 W at 534.8 nm. In the following 50 mm long DKDP crystal, more than 50 µW of light at 267.4 nm are generated. An upper limit for the passive short-term phase stability has been measured by a beat-node measurement with an existing phase-stabilized quadrupling system employing the same source laser. The resulting fractional frequency instability of less than 5×10-17 after 1 s supports lifetime-limited probing of the 27Al+ clock transition, given a sufficiently stable laser source. A further improved stability of the fourth harmonic light is expected through interferometric path length stabilisation of the pump light by back-reflecting it through the entire setup and correcting for frequency deviations. The in-loop error signal indicates an electronically limited instability of 1 × 10-18 at 1 s.
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Bai SY, An JH. Generating Stable Spin Squeezing by Squeezed-Reservoir Engineering. PHYSICAL REVIEW LETTERS 2021; 127:083602. [PMID: 34477431 DOI: 10.1103/physrevlett.127.083602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Revised: 07/13/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that N two-level systems (TLSs) located near a one-dimensional waveguide can generate SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent driving on the TLSs. Incorporating the mediation role of the common waveguide and the technique of squeezed-reservoir engineering, our scheme exhibits the advantages over previous ones in the scaling relation of the SS parameter with the number of the TLSs. The long-range correlation feature of the generated SS along the waveguide in our scheme may endow it with certain superiority in quantum sensing, e.g., improving the sensing efficiency of spatially unidentified weak magnetic fields.
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Affiliation(s)
- Si-Yuan Bai
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Jun-Hong An
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 2020; 588:408-413. [PMID: 33328666 DOI: 10.1038/s41586-020-3009-y] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 09/17/2020] [Indexed: 11/09/2022]
Abstract
The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology1, simulation2 and information3. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems2,4-7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms8-10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 1016. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel11,12. The result is a relative fractional frequency stability of 5.2(3) × 10-17τ-1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition13 in tailored atom arrays.
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8
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Schulte M, Lisdat C, Schmidt PO, Sterr U, Hammerer K. Prospects and challenges for squeezing-enhanced optical atomic clocks. Nat Commun 2020; 11:5955. [PMID: 33235213 PMCID: PMC7686368 DOI: 10.1038/s41467-020-19403-7] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2020] [Accepted: 10/02/2020] [Indexed: 11/18/2022] Open
Abstract
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.
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Affiliation(s)
- Marius Schulte
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Appelstrasse 2, 30167, Hannover, Germany.
| | - Christian Lisdat
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
| | - Piet O Schmidt
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
- Institute for Quantum Optics, Leibniz University Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Uwe Sterr
- Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany
| | - Klemens Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert-Einstein-Institute), Leibniz University Hannover, Appelstrasse 2, 30167, Hannover, Germany.
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9
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Pezzè L, Smerzi A. Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol. PHYSICAL REVIEW LETTERS 2020; 125:210503. [PMID: 33274961 DOI: 10.1103/physrevlett.125.210503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 09/29/2020] [Indexed: 06/12/2023]
Abstract
We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.
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Affiliation(s)
- Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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10
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Rossi MAC, Albarelli F, Tamascelli D, Genoni MG. Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement. PHYSICAL REVIEW LETTERS 2020; 125:200505. [PMID: 33258625 DOI: 10.1103/physrevlett.125.200505] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2020] [Accepted: 10/19/2020] [Indexed: 06/12/2023]
Abstract
We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.
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Affiliation(s)
- Matteo A C Rossi
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
| | - Francesco Albarelli
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
| | - Dario Tamascelli
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, I-20133 Milano, Italy
| | - Marco G Genoni
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, I-20133 Milano, Italy
- INFN - Sezione di Milano, I-20133 Milano, Italy
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11
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Alexander B, Bollinger JJ, Uys H. Generating Greenberger-Horne-Zeilinger states with squeezing and postselection. PHYSICAL REVIEW. A 2020; 101:10.1103/PhysRevA.101.062303. [PMID: 34796312 PMCID: PMC8597541 DOI: 10.1103/physreva.101.062303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Many quantum state preparation methods rely on a combination of dissipative quantum state initialization followed by unitary evolution to a desired target state. Here we demonstrate the usefulness of quantum measurement as an additional tool for quantum state preparation. Starting from a pure separable multipartite state, a control sequence, which includes rotation, spin squeezing via one-axis twisting, quantum measurement, and postselection, generates highly entangled multipartite states, which we refer to as projected squeezed (PS) states. Through an optimization method, we then identify parameters required to maximize the overlap fidelity of the PS states with the maximally entangled Greenberger-Horne-Zeilinger (GHZ) states. The method leads to an appreciable decrease in the state preparation time of GHZ states for successfully postselected outcomes when compared to preparation through unitary evolution with one-axis twisting only.
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Affiliation(s)
- Byron Alexander
- Department of Physics, Stellenbosch University, Stellenbosch Central 7600, Stellenbosch, South Africa
| | - John J. Bollinger
- National Institute of Standards and Technology, Boulder, Colorado 80305, USA
| | - Hermann Uys
- Department of Physics, Stellenbosch University, Stellenbosch Central 7600, Stellenbosch, South Africa
- Council for Scientific and Industrial Research, National Laser Centre, Brummeria, Pretoria 0184, South Africa
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12
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Borish V, Marković O, Hines JA, Rajagopal SV, Schleier-Smith M. Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas. PHYSICAL REVIEW LETTERS 2020; 124:063601. [PMID: 32109106 DOI: 10.1103/physrevlett.124.063601] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Accepted: 01/09/2020] [Indexed: 06/10/2023]
Abstract
We report on the realization of long-range Ising interactions in a cold gas of cesium atoms by Rydberg dressing. The interactions are enhanced by coupling to Rydberg states in the vicinity of a Förster resonance. We characterize the interactions by measuring the mean-field shift of the clock transition via Ramsey spectroscopy, observing one-axis twisting dynamics. We furthermore emulate a transverse-field Ising model by periodic application of a microwave field and detect dynamical signatures of the paramagnetic-ferromagnetic phase transition. Our results highlight the power of optical addressing for achieving local and dynamical control of interactions, enabling prospects ranging from investigating Floquet quantum criticality to producing tunable-range spin squeezing.
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Affiliation(s)
- V Borish
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - O Marković
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - J A Hines
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - S V Rajagopal
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - M Schleier-Smith
- Department of Physics, Stanford University, Stanford, California 94305, USA
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13
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Tensor-network approach for quantum metrology in many-body quantum systems. Nat Commun 2020; 11:250. [PMID: 31937760 PMCID: PMC6959326 DOI: 10.1038/s41467-019-13735-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Accepted: 11/21/2019] [Indexed: 12/02/2022] Open
Abstract
Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions. The maximum precision achievable in quantum metrology is in general tractable only in few-body scenarios or in case of uncorrelated local noise. Here, the authors show a tensor networks method to compute such bounds in cases with large number of probes and short-range spatial and temporal noise correlations.
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14
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Kura N, Ueda M. Standard Quantum Limit and Heisenberg Limit in Function Estimation. PHYSICAL REVIEW LETTERS 2020; 124:010507. [PMID: 31976685 DOI: 10.1103/physrevlett.124.010507] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2019] [Indexed: 06/10/2023]
Abstract
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology for a spatially varying phase operator, where various degrees of smooth functions are considered. The error bounds are identified in the cases of the absence and the presence of interparticle entanglement, which correspond to the standard quantum limit and the Heisenberg limit, respectively. Notably, these error bounds can be reached by either position-localized states or wave-number-localized ones. In fact, we show that these error bounds are theoretically optimal for any type of probe states, indicating that quantum metrology on functions is also subject to the Nyquist-Shannon sampling theorem, even if classical detection is replaced by quantum measurement.
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Affiliation(s)
- Naoto Kura
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
| | - Masahito Ueda
- Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
- RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
- Institute for Physics of Intelligence, University of Tokyo, 7-3-1 Hongo, Bunkyou-ku, Tokyo 113-0033, Japan
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15
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Megidish E, Broz J, Greene N, Häffner H. Improved Test of Local Lorentz Invariance from a Deterministic Preparation of Entangled States. PHYSICAL REVIEW LETTERS 2019; 122:123605. [PMID: 30978053 DOI: 10.1103/physrevlett.122.123605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Indexed: 06/09/2023]
Abstract
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using ^{40}Ca^{+} ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe, for bipartite entangled states, the expected gain of a factor of two in the precision. Under specific conditions, multipartite entangled states may yield substantial further improvements. Our measurements improve the previous best limit for local Lorentz invariance of the electron using ^{40}Ca^{+} ions by a factor of two to four to about 5×10^{-19}.
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Affiliation(s)
- Eli Megidish
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Joseph Broz
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Nicole Greene
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Hartmut Häffner
- Department of Physics, University of California, Berkeley, California 94720, USA
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16
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Davis EJ, Wang Z, Safavi-Naeini AH, Schleier-Smith MH. Painting Nonclassical States of Spin or Motion with Shaped Single Photons. PHYSICAL REVIEW LETTERS 2018; 121:123602. [PMID: 30296158 DOI: 10.1103/physrevlett.121.123602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Indexed: 06/08/2023]
Abstract
We propose a robust scheme for generating macroscopic superposition states of spin or motion with the aid of a single photon. Shaping the wave packet of the photon enables high-fidelity preparation of nonclassical states of matter even in the presence of photon loss. Success is heralded by photodetection, enabling the scheme to be implemented with a weak coherent field. We analyze applications to preparing Schrödinger cat states of a collective atomic spin or of a mechanical oscillator coupled to an optical resonator. The method generalizes to preparing arbitrary superpositions of coherent states, enabling full quantum control. We illustrate this versatility by showing how to prepare Dicke or Fock states, as well as superpositions in the Dicke or Fock basis.
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Affiliation(s)
- Emily J Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Zhaoyou Wang
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
| | - Amir H Safavi-Naeini
- Department of Applied Physics, Stanford University, Stanford, California 94305, USA
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17
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Mehlstäubler TE, Grosche G, Lisdat C, Schmidt PO, Denker H. Atomic clocks for geodesy. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2018; 81:064401. [PMID: 29667603 DOI: 10.1088/1361-6633/aab409] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We review experimental progress on optical atomic clocks and frequency transfer, and consider the prospects of using these technologies for geodetic measurements. Today, optical atomic frequency standards have reached relative frequency inaccuracies below 10-17, opening new fields of fundamental and applied research. The dependence of atomic frequencies on the gravitational potential makes atomic clocks ideal candidates for the search for deviations in the predictions of Einstein's general relativity, tests of modern unifying theories and the development of new gravity field sensors. In this review, we introduce the concepts of optical atomic clocks and present the status of international clock development and comparison. Besides further improvement in stability and accuracy of today's best clocks, a large effort is put into increasing the reliability and technological readiness for applications outside of specialized laboratories with compact, portable devices. With relative frequency uncertainties of 10-18, comparisons of optical frequency standards are foreseen to contribute together with satellite and terrestrial data to the precise determination of fundamental height reference systems in geodesy with a resolution at the cm-level. The long-term stability of atomic standards will deliver excellent long-term height references for geodetic measurements and for the modelling and understanding of our Earth.
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Affiliation(s)
- Tanja E Mehlstäubler
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
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18
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Eldredge Z, Foss-Feig M, Gross JA, Rolston SL, Gorshkov AV. Optimal and secure measurement protocols for quantum sensor networks. PHYSICAL REVIEW. A 2018; 97:10.1103/PhysRevA.97.042337. [PMID: 31093589 PMCID: PMC6513338 DOI: 10.1103/physreva.97.042337] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
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Affiliation(s)
- Zachary Eldredge
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Jonathan A Gross
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - S L Rolston
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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19
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Choi S, Yao NY, Lukin MD. Dynamical Engineering of Interactions in Qudit Ensembles. PHYSICAL REVIEW LETTERS 2017; 119:183603. [PMID: 29219566 DOI: 10.1103/physrevlett.119.183603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2017] [Indexed: 06/07/2023]
Abstract
We propose and analyze a method to engineer effective interactions in an ensemble of d-level systems (qudits) driven by global control fields. In particular, we present (i) a necessary and sufficient condition under which a given interaction can be decoupled, (ii) the existence of a universal sequence that decouples any (cancelable) interaction, and (iii) an efficient algorithm to engineer a target Hamiltonian from an initial Hamiltonian (if possible). We illustrate the potential of this method with two examples. Specifically, we present a 6-pulse sequence that decouples effective spin-1 dipolar interactions and demonstrate that a spin-1 Ising chain can be engineered to study transitions among three distinct symmetry protected topological phases. Our work enables new approaches for the realization of both many-body quantum memories and programmable analog quantum simulators using existing experimental platforms.
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Affiliation(s)
- Soonwon Choi
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Norman Y Yao
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
| | - Mikhail D Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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20
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Eldredge Z, Gong ZX, Young JT, Moosavian AH, Foss-Feig M, Gorshkov AV. Fast Quantum State Transfer and Entanglement Renormalization Using Long-Range Interactions. PHYSICAL REVIEW LETTERS 2017; 119:170503. [PMID: 29219445 PMCID: PMC6467282 DOI: 10.1103/physrevlett.119.170503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2016] [Indexed: 05/31/2023]
Abstract
In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speedup possible is an open question. In this Letter, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with a strength bounded by 1/r^{α}. If α
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Affiliation(s)
- Zachary Eldredge
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Zhe-Xuan Gong
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, Colorado School of Mines, Golden, Colorado 80401, USA
| | - Jeremy T Young
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Ali Hamed Moosavian
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute and Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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21
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Matei DG, Legero T, Häfner S, Grebing C, Weyrich R, Zhang W, Sonderhouse L, Robinson JM, Ye J, Riehle F, Sterr U. 1.5 μm Lasers with Sub-10 mHz Linewidth. PHYSICAL REVIEW LETTERS 2017; 118:263202. [PMID: 28707932 DOI: 10.1103/physrevlett.118.263202] [Citation(s) in RCA: 116] [Impact Index Per Article: 16.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Indexed: 06/07/2023]
Abstract
We report on two ultrastable lasers each stabilized to independent silicon Fabry-Pérot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of 4×10^{-17} for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergences encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 to 55 s.
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Affiliation(s)
- D G Matei
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - T Legero
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - S Häfner
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - C Grebing
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - R Weyrich
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - W Zhang
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, 440 UCB, Boulder, Colorado 80309, USA
| | - L Sonderhouse
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, 440 UCB, Boulder, Colorado 80309, USA
| | - J M Robinson
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, 440 UCB, Boulder, Colorado 80309, USA
| | - J Ye
- JILA, National Institute of Standards and Technology and University of Colorado, Department of Physics, 440 UCB, Boulder, Colorado 80309, USA
| | - F Riehle
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
| | - U Sterr
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
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22
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Sekatski P, Skotiniotis M, Dür W. Improved Sensing with a Single Qubit. PHYSICAL REVIEW LETTERS 2017; 118:170801. [PMID: 28498713 DOI: 10.1103/physrevlett.118.170801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2016] [Indexed: 06/07/2023]
Abstract
We consider quantum metrology with arbitrary prior knowledge of the parameter. We demonstrate that a single sensing two-level system can act as a virtual multilevel system that offers increased sensitivity in a Bayesian single-shot metrology scenario, and that allows one to estimate (arbitrary) large parameter values by avoiding phase wraps. This is achieved by making use of additional degrees of freedom or auxiliary systems not participating in the sensing process. The joint system is manipulated by intermediate control operations in such a way that an effective Hamiltonian, with an arbitrary spectrum, is generated that mimics the spectrum of a multisystem interacting with the field. We show how to use additional internal degrees of freedom of a single trapped ion to achieve a high-sensitivity magnetic field sensor for fields with arbitrary prior knowledge.
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Affiliation(s)
- P Sekatski
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria
| | - M Skotiniotis
- Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
| | - W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria
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23
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Yao Y, Jiang Y, Yu H, Bi Z, Ma L. Optical frequency divider with division uncertainty at the 10−21 level. Natl Sci Rev 2016. [DOI: 10.1093/nsr/nww063] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
Abstract
Optical clocks with unprecedented accuracy of 10−18 promise innovations in many research areas. Their applications rely to a large extent on the ability of precisely converting the frequency from one optical clock to another, or particularly to the frequencies in the fiber telecom band for long-distance transmission. This report demonstrates a low-noise, high-precision optical frequency divider, which realizes accurate optical frequency conversion and enables precise measurement of optical frequency ratios. By measuring against the frequency ratio between the fundamental and the second harmonic of a 1064-nm laser instead of a second copy of the same system, we demonstrate that the optical frequency divider has a fractional frequency division instability of 6 × 10−19 at 1 s and a fractional frequency division uncertainty of 1.4 × 10−21. The remarkable numbers can support frequency division of the best optical clocks in the world without frequency-conversion-caused degradation of their performance.
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Affiliation(s)
- Yuan Yao
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Yanyi Jiang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Hongfu Yu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Zhiyi Bi
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Longsheng Ma
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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24
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Magnetic field sensing subject to correlated noise with a ring spin chain. Sci Rep 2016; 6:33254. [PMID: 27623048 PMCID: PMC5020690 DOI: 10.1038/srep33254] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2016] [Accepted: 08/24/2016] [Indexed: 11/08/2022] Open
Abstract
In this paper, we focus on the magnetic field sensing subject to a correlated noise. We use a ring spin chain with only the nearest neighbor interactions as our probe to estimate both the intensity B and the direction θ of the magnetic field when the probe reaches its steady state. We numerically calculate the quantum Fisher information (QFI) to characterize the estimation precision. On the one hand, for estimating B, we find that the coupling between spins in the probe plays an important role in the precision, and the largest value of the QFI can be achieved when θ = π/2 together with an optimal coupling. Moreover, for any direction, the precision scaling can be better than the Heisenberg-limit (HL) with a proper coupling. On the other hand, for estimating θ, we find that our probe can perform a high precision detection for θ ~ π/2, with the QFI much larger than that for any other directions, especially when the coupling is tuned to the optimal value. And we find that the precision scaling for θ ~ π/2 can be better than the HL, but for other directions, the precision scaling is only limited to the standard quantum limit (SQL). Due to the computational complexity we restrict the number of spins in the probe to 60.
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25
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Kómár P, Topcu T, Kessler EM, Derevianko A, Vuletić V, Ye J, Lukin MD. Quantum Network of Atom Clocks: A Possible Implementation with Neutral Atoms. PHYSICAL REVIEW LETTERS 2016; 117:060506. [PMID: 27541452 DOI: 10.1103/physrevlett.117.060506] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2016] [Indexed: 06/06/2023]
Abstract
We propose a protocol for creating a fully entangled Greenberger-Horne-Zeilinger-type state of neutral atoms in spatially separated optical atomic clocks. In our scheme, local operations make use of the strong dipole-dipole interaction between Rydberg excitations, which give rise to fast and reliable quantum operations involving all atoms in the ensemble. The necessary entanglement between distant ensembles is mediated by single-photon quantum channels and collectively enhanced light-matter couplings. These techniques can be used to create the recently proposed quantum clock network based on neutral atom optical clocks. We specifically analyze a possible realization of this scheme using neutral Yb ensembles.
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Affiliation(s)
- P Kómár
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
| | - T Topcu
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, University of Nevada, Reno, Nevada 89557, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - E M Kessler
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - A Derevianko
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
- Department of Physics, University of Nevada, Reno, Nevada 89557, USA
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - V Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - J Ye
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - M D Lukin
- Physics Department, Harvard University, Cambridge, Massachusetts 02138, USA
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Abstract
Abstract
Precision measurement and frequency metrology have pushed many scientific and technological frontiers in the field of atomic, molecular and optical physics. In this article, we provide a brief review on the recent development of optical atomic clocks, with an emphasis placed on the important inter-dependence between measurement precision and systematic effects. After presenting a general discussion on the motivation and techniques behind the development of optical lattice clocks, where the use of many atoms greatly enhances the measurement precision, we present the JILA strontium optical lattice clock as the leading system of frequency metrology with the lowest total uncertainty, and we describe other related research activities. We discuss key ingredients that have enabled the optical lattice clocks with ultracold atoms to reach the 18th digit in both precision and accuracy. Furthermore, we discuss extending the power of precision clock spectroscopy to study quantum many-body physics and to provide control for atomic quantum materials. In addition, we explore future research directions that have the potential to achieve even greater precision.
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Affiliation(s)
- Xibo Zhang
- JILA, NIST and University of Colorado, 440 UCB, Boulder, CO 80309, USA
| | - Jun Ye
- JILA, NIST and University of Colorado, 440 UCB, Boulder, CO 80309, USA
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27
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Lindkvist J, Sabín C, Johansson G, Fuentes I. Motion and gravity effects in the precision of quantum clocks. Sci Rep 2015; 5:10070. [PMID: 25988238 PMCID: PMC4437316 DOI: 10.1038/srep10070] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Accepted: 03/27/2015] [Indexed: 11/09/2022] Open
Abstract
We show that motion and gravity affect the precision of quantum clocks. We consider a localised quantum field as a fundamental model of a quantum clock moving in spacetime and show that its state is modified due to changes in acceleration. By computing the quantum Fisher information we determine how relativistic motion modifies the ultimate bound in the precision of the measurement of time. While in the absence of motion the squeezed vacuum is the ideal state for time estimation, we find that it is highly sensitive to the motion-induced degradation of the quantum Fisher information. We show that coherent states are generally more resilient to this degradation and that in the case of very low initial number of photons, the optimal precision can be even increased by motion. These results can be tested with current technology by using superconducting resonators with tunable boundary conditions.
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Affiliation(s)
- Joel Lindkvist
- Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-41296 Göteborg, Sweden
| | - Carlos Sabín
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingam NG7 2RD, United Kingdom
| | - Göran Johansson
- Microtechnology and Nanoscience, MC2, Chalmers University of Technology, S-41296 Göteborg, Sweden
| | - Ivette Fuentes
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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28
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Low GH, Yoder TJ, Chuang IL. Quantum imaging by coherent enhancement. PHYSICAL REVIEW LETTERS 2015; 114:100801. [PMID: 25815918 DOI: 10.1103/physrevlett.114.100801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2014] [Indexed: 06/04/2023]
Abstract
Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the coherence time of the system should be made short, and that the statistical scaling ∼1/√t defines the resolution limit for imaging time t. However, here we show in contrast that given the same resources, a long coherence time permits a higher resolution image. In this quantum regime, we give a procedure for determining the position of a single two-level system and demonstrate that the standard errors of our position estimates scale at the Heisenberg limit as ∼1/t, a quadratic, and notably optimal, improvement over the classical case.
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Affiliation(s)
- Guang Hao Low
- Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Theodore J Yoder
- Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Isaac L Chuang
- Center for Ultracold Atoms, Research Laboratory of Electronics, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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29
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Fitting magnetic field gradient with Heisenberg-scaling accuracy. Sci Rep 2014; 4:7390. [PMID: 25487218 PMCID: PMC4260217 DOI: 10.1038/srep07390] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2014] [Accepted: 11/20/2014] [Indexed: 11/27/2022] Open
Abstract
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
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30
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Quantum-enhanced metrology for multiple phase estimation with noise. Sci Rep 2014; 4:5933. [PMID: 25090445 PMCID: PMC4123202 DOI: 10.1038/srep05933] [Citation(s) in RCA: 52] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2014] [Accepted: 07/14/2014] [Indexed: 11/29/2022] Open
Abstract
We present a general quantum metrology framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase estimation. Our results show that simultaneous estimation (SE) of multiple phases is always better than individual estimation (IE) of each phase even in noisy environment. The utility of the bounds of multiple phase estimation for photon loss channels is exemplified explicitly. When noise is low, those bounds possess the Heisenberg scale showing quantum-enhanced precision with the O(d) advantage for SE, where d is the number of phases. However, this O(d) advantage of SE scheme in the variance of the estimation may disappear asymptotically when photon loss becomes significant and then only a constant advantage over that of IE scheme demonstrates. Potential application of those results is presented.
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