1
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Laha P, Moore DW, Filip R. Entanglement Growth via Splitting of a Few Thermal Quanta. PHYSICAL REVIEW LETTERS 2024; 132:210201. [PMID: 38856241 DOI: 10.1103/physrevlett.132.210201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Revised: 02/20/2024] [Accepted: 04/08/2024] [Indexed: 06/11/2024]
Abstract
Quanta splitting is an essential generator of Gaussian entanglement, exemplified by Einstein-Podolsky-Rosen states and apparently the most commonly occurring form of entanglement. In general, it results from the strong pumping of a nonlinear process with a highly coherent and low-noise external drive. In contrast, recent experiments involving efficient trilinear processes in trapped ions and superconducting circuits have opened the complementary possibility to test the splitting of a few thermal quanta. Stimulated by such small thermal energy, a strong degenerate trilinear coupling generates large amounts of nonclassicality, detectable by more than 3 dB of distillable quadrature squeezing. Substantial entanglement can be generated via frequent passive linear coupling to a third mode present in parallel with the trilinear coupling. This new form of entanglement, outside any Gaussian approximation, surprisingly grows with the mean number of split thermal quanta; a quality absent from Gaussian entanglement. Using distillable squeezing we shed light on this new entanglement mechanism for nonlinear bosonic systems.
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Affiliation(s)
- Pradip Laha
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - Darren W Moore
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - Radim Filip
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
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2
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Downing CA, Vidiella-Barranco A. Parametrically driving a quantum oscillator into exceptionality. Sci Rep 2023; 13:11004. [PMID: 37419917 PMCID: PMC10329046 DOI: 10.1038/s41598-023-37964-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2023] [Accepted: 06/30/2023] [Indexed: 07/09/2023] Open
Abstract
The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.
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Affiliation(s)
- C A Downing
- Department of Physics and Astronomy, University of Exeter, Exeter, EX4 4QL, UK.
| | - A Vidiella-Barranco
- Gleb Wataghin Institute of Physics, University of Campinas - UNICAMP, Campinas, SP, 13083-859, Brazil
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3
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Nikitchuk BY, Anikin EV, Maslova NS, Gippius NA. The symmetry in the model of two coupled Kerr oscillators leads to simultaneous multi-photon transitions. Sci Rep 2023; 13:2997. [PMID: 36810462 PMCID: PMC9944305 DOI: 10.1038/s41598-023-30197-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/17/2023] [Indexed: 02/23/2023] Open
Abstract
We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere.
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Affiliation(s)
- Bogdan Y Nikitchuk
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia.
- Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Moscow Region, Russia.
| | - Evgeny V Anikin
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
- Russian Quantum Center, 121205, Moscow, Russia
| | - Natalya S Maslova
- Quantum Technology Centrum, Department of Physics, Lomonosov Moscow State University, 119991, Moscow, Russia
| | - Nikolay A Gippius
- Skolkovo Institute of Science and Technology, 121205, Moscow, Russia
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4
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Ornigotti L, Filip R. Stroboscopic thermally-driven mechanical motion. Sci Rep 2022; 12:20091. [PMID: 36418396 PMCID: PMC9684504 DOI: 10.1038/s41598-022-24074-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 11/09/2022] [Indexed: 11/25/2022] Open
Abstract
Unstable nonlinear systems can produce a large displacement driven by a small thermal initial noise. Such inherently nonlinear phenomena are stimulating in stochastic physics, thermodynamics, and in the future even in quantum physics. In one-dimensional mechanical instabilities, recently made available in optical levitation, the rapidly increasing noise accompanying the unstable motion reduces a displacement signal already in its detection. It limits the signal-to-noise ratio for upcoming experiments, thus constraining the observation of such essential nonlinear phenomena and their further exploitation. An extension to a two-dimensional unstable dynamics helps to separate the desired displacement from the noisy nonlinear driver to two independent variables. It overcomes the limitation upon observability, thus enabling further exploitation. However, the nonlinear driver remains unstable and rapidly gets noisy. It calls for a challenging high-order potential to confine the driver dynamics and rectify the noise. Instead, we propose and analyse a feasible stroboscopically-cooled driver that provides the desired detectable motion with sufficiently high signal-to-noise ratio. Fast and deep cooling, together with a rapid change of the driver stiffness, are required to reach it. However, they have recently become available in levitating optomechanics. Therefore, our analysis finally opens the road to experimental investigation of thermally-driven motion in nonlinear systems, its thermodynamical analysis, and future quantum extensions.
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Affiliation(s)
- Luca Ornigotti
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic.
- Quantum Optics, Quantum Nanophysics and Quantum Information, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090, Wien, Austria.
| | - Radim Filip
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46, Olomouc, Czech Republic
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5
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Podhora L, Lachman L, Pham T, Lešundák A, Číp O, Slodička L, Filip R. Quantum Non-Gaussianity of Multiphonon States of a Single Atom. PHYSICAL REVIEW LETTERS 2022; 129:013602. [PMID: 35841581 DOI: 10.1103/physrevlett.129.013602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Revised: 03/22/2022] [Accepted: 05/25/2022] [Indexed: 06/15/2023]
Abstract
Quantum non-Gaussian mechanical states are already required in a range of applications. The discrete building blocks of such states are the energy eigenstates-Fock states. Despite progress in their preparation, the remaining imperfections can still invisibly cause loss of the aspects critical for their applications. We derive and apply the most challenging hierarchy of quantum non-Gaussian criteria on the characterization of single trapped-ion oscillator mechanical Fock states with up to 10 phonons. We analyze the depth of these quantum non-Gaussian features under intrinsic mechanical heating and predict their requirement for reaching quantum advantage in the sensing of a mechanical force.
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Affiliation(s)
- L Podhora
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - L Lachman
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - T Pham
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - A Lešundák
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - O Číp
- Institute of Scientific Instruments of the Czech Academy of Sciences, Královopolská 147, 612 64 Brno, Czech Republic
| | - L Slodička
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
| | - R Filip
- Department of Optics, Palacký University, 17. listopadu 12, 77146 Olomouc, Czech Republic
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6
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Phase-space studies of backscattering diffraction of defective Schrödinger cat states. Sci Rep 2021; 11:11619. [PMID: 34078940 PMCID: PMC8172851 DOI: 10.1038/s41598-021-90738-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 05/17/2021] [Indexed: 11/08/2022] Open
Abstract
The coherent superposition of two well separated Gaussian wavepackets, with defects caused by their imperfect preparation, is considered within the phase-space approach based on the Wigner distribution function. This generic state is called the defective Schrödinger cat state due to this imperfection which significantly modifies the interference term. Propagation of this state in the phase space is described by the Moyal equation which is solved for the case of a dispersive medium with a Gaussian barrier in the above-barrier reflection regime. Formally, this regime constitutes conditions for backscattering diffraction phenomena. Dynamical quantumness and the degree of localization in the phase space of the considered state as a function of its imperfection are the subject of the performed analysis. The obtained results allow concluding that backscattering communication based on the defective Schrödinger cat states appears to be feasible with existing experimental capabilities.
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7
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Controls of a superconducting quantum parametron under a strong pump field. Sci Rep 2021; 11:11459. [PMID: 34075132 PMCID: PMC8169783 DOI: 10.1038/s41598-021-90874-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 05/17/2021] [Indexed: 11/08/2022] Open
Abstract
Pumped at approximately twice the natural frequency, a Josephson parametric oscillator called parametron or Kerr parametric oscillator shows self-oscillation. Quantum annealing and universal quantum computation using self-oscillating parametrons as qubits were proposed. However, controls of parametrons under the pump field are degraded by unwanted rapidly oscillating terms in the Hamiltonian, which we call non-resonant rapidly oscillating terms (NROTs) coming from the violation of the rotating wave approximation. Therefore, the pump field can be an intrinsic origin of the imperfection of controls of parametrons. Here, we theoretically study the influence of the NROTs on the accuracy of controls of a parametron: a cat-state creation and a single-qubit gate. It is shown that there is a trade-off relationship between the suppression of the nonadiabatic transitions and the validity of the rotating wave approximation in a conventional approach. We also show that the tailored time dependence of the detuning of the pump field can suppress both of the nonadiabatic transitions and the disturbance of the state of the parametron due to the NROTs.
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8
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Lachman L, Filip R. Quantum Non-Gaussian Photon Coincidences. PHYSICAL REVIEW LETTERS 2021; 126:213604. [PMID: 34114867 DOI: 10.1103/physrevlett.126.213604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2020] [Accepted: 04/21/2021] [Indexed: 06/12/2023]
Abstract
Photon coincidences represent an important resource for quantum technologies. They expose nonlinear quantum processes in matter and are essential for sources of entanglement. We derive broadly applicable criteria for quantum non-Gaussian two-photon coincidences that certify a new quality of photon sources. The criteria reject states emerging from Gaussian parametric processes, which often limit applications in quantum technologies. We also analyze the robustness of the quantum non-Gaussian coincidences and compare it to the heralded quantum non-Gaussianity of single photons based on them.
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Affiliation(s)
- Lukáš Lachman
- Department of Optics, Faculty of Science, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - Radim Filip
- Department of Optics, Faculty of Science, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
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9
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Qiao M, Wang Y, Cai Z, Du B, Wang P, Luan C, Chen W, Noh HR, Kim K. Double-Electromagnetically-Induced-Transparency Ground-State Cooling of Stationary Two-Dimensional Ion Crystals. PHYSICAL REVIEW LETTERS 2021; 126:023604. [PMID: 33512231 DOI: 10.1103/physrevlett.126.023604] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2020] [Accepted: 12/21/2020] [Indexed: 06/12/2023]
Abstract
We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8) ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.
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Affiliation(s)
- Mu Qiao
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Ye Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
| | - Zhengyang Cai
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Botao Du
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Pengfei Wang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Chunyang Luan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Wentao Chen
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
| | - Heung-Ryoul Noh
- Department of Physics, Chonnam National University, Gwangju 61186, Korea
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China
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10
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Sarkar P, Bhattacharjee JK. Nonlinear parametric oscillator: A tool for probing quantum fluctuations. Phys Rev E 2020; 102:052204. [PMID: 33327191 DOI: 10.1103/physreve.102.052204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 10/15/2020] [Indexed: 06/12/2023]
Abstract
Nanomechanical oscillators have, over the last few years, started probing regimes where quantum fluctuations are important. Here we consider a nonlinear parametric oscillator in the quantum domain. We show that in the classical subharmonic resonance zone, the quantum fluctuations are finite but greatly magnified depending on the strength of the nonlinear coupling. This should make such oscillators useful in probing quantum fluctuations.
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Affiliation(s)
- Prasun Sarkar
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700 032, India
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11
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Flühmann C, Home JP. Direct Characteristic-Function Tomography of Quantum States of the Trapped-Ion Motional Oscillator. PHYSICAL REVIEW LETTERS 2020; 125:043602. [PMID: 32794777 DOI: 10.1103/physrevlett.125.043602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2019] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
We implement direct readout of the symmetric characteristic function of quantum states of the motional oscillation of a trapped calcium ion. Suitably chosen internal state rotations combined with internal state-dependent displacements, based on bichromatic laser fields, map the expectation value of the real or imaginary part of the displacement operator to the internal states, which are subsequently read out. Combining these results provides full information about the symmetric characteristic function. We characterize the technique by applying it to a range of archetypal quantum oscillator states, including displaced and squeezed Gaussian states as well as two and three component superpositions of displaced squeezed states. For each, we discuss relevant features of the characteristic function and Wigner phase-space quasiprobability distribution. The direct reconstruction of these highly nonclassical oscillator states using a reduced number of measurements is an essential tool for understanding and optimizing the control of oscillator systems for quantum sensing and quantum information applications.
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Affiliation(s)
- C Flühmann
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
| | - J P Home
- Institute for Quantum Electronics, ETH Zürich, Otto-Stern-Weg 1, 8093 Zürich, Switzerland
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12
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Tamura M, Mukaiyama T, Toyoda K. Quantum Walks of a Phonon in Trapped Ions. PHYSICAL REVIEW LETTERS 2020; 124:200501. [PMID: 32501043 DOI: 10.1103/physrevlett.124.200501] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2019] [Accepted: 04/22/2020] [Indexed: 06/11/2023]
Abstract
We report the observation of the quantum walks of a phonon, a vibrational quantum, in a trapped-ion crystal. By employing the capability to prepare and observe the localized wave packet of a phonon, the propagation of a single radial local phonon in a four-ion linear crystal is observed with single-site resolution. The results show an agreement with numerical calculations, indicating the predictability and reproducibility of the phonon system. These characteristics may contribute advantageously in the advanced studies of quantum walks, as well as boson sampling and quantum simulation.
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Affiliation(s)
- Masaya Tamura
- Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
| | - Takashi Mukaiyama
- Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan
- Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Toyonaka 560-8531, Japan
| | - Kenji Toyoda
- Center for Quantum Information and Quantum Biology, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, Toyonaka 560-8531, Japan
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13
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Gan HCJ, Maslennikov G, Tseng KW, Nguyen C, Matsukevich D. Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System. PHYSICAL REVIEW LETTERS 2020; 124:170502. [PMID: 32412255 DOI: 10.1103/physrevlett.124.170502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2019] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.
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Affiliation(s)
- H C J Gan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Ko-Wei Tseng
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Chihuan Nguyen
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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14
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Frimmer M, Heugel TL, Nosan Ž, Tebbenjohanns F, Hälg D, Akin A, Degen CL, Novotny L, Chitra R, Zilberberg O, Eichler A. Rapid Flipping of Parametric Phase States. PHYSICAL REVIEW LETTERS 2019; 123:254102. [PMID: 31922787 DOI: 10.1103/physrevlett.123.254102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Indexed: 06/10/2023]
Abstract
We experimentally demonstrate flipping the phase state of a parametron within a single period of its oscillation. A parametron is a binary logic element based on a driven nonlinear resonator. It features two stable phase states that define an artificial spin. The most basic operation performed on a parametron is a bit flip between these two states. Thus far, this operation involved changing the energetic population of the resonator and therefore required a number of oscillations on the order of the quality factor Q. Our technique takes a radically different approach and relies on rapid control of the underlying potential. Our work represents a paradigm shift for phase-encoded logic operations by boosting the speed of a parametron bit flip to its ultimate limit.
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Affiliation(s)
- Martin Frimmer
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Toni L Heugel
- Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Žiga Nosan
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | | | - David Hälg
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Abdulkadir Akin
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Christian L Degen
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, CH-8093 Zürich, Switzerland
| | - R Chitra
- Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Oded Zilberberg
- Institute for Theoretical Physics, ETH Zürich, CH-8093 Zürich, Switzerland
| | - Alexander Eichler
- Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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15
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Maslennikov G, Ding S, Hablützel R, Gan J, Roulet A, Nimmrichter S, Dai J, Scarani V, Matsukevich D. Quantum absorption refrigerator with trapped ions. Nat Commun 2019; 10:202. [PMID: 30643131 PMCID: PMC6331551 DOI: 10.1038/s41467-018-08090-0] [Citation(s) in RCA: 56] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Accepted: 12/07/2018] [Indexed: 11/09/2022] Open
Abstract
In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime made possible by coherence and demonstrate cooling below both the steady-state energy and a benchmark set by classical thermodynamics.
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Affiliation(s)
- Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore.,JILA, National Institute of Standards and Technology and University of Colorado, and Department of Physics, University of Colorado, Boulder, CO, 80309, USA
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Jaren Gan
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Alexandre Roulet
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Stefan Nimmrichter
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Jibo Dai
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore
| | - Valerio Scarani
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore.,Department of Physics, National University of Singapore, 2 Science Dr 3, Singapore, 117551, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Dr 2, Singapore, 117543, Singapore. .,Department of Physics, National University of Singapore, 2 Science Dr 3, Singapore, 117551, Singapore.
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16
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Zhang J, Um M, Lv D, Zhang JN, Duan LM, Kim K. NOON States of Nine Quantized Vibrations in Two Radial Modes of a Trapped Ion. PHYSICAL REVIEW LETTERS 2018; 121:160502. [PMID: 30387619 DOI: 10.1103/physrevlett.121.160502] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2017] [Revised: 07/25/2018] [Indexed: 06/08/2023]
Abstract
We develop a deterministic method to generate and verify arbitrarily high NOON states of quantized vibrations (phonons), through the coupling to the internal state. We experimentally create the entangled states up to N=9 phonons in two vibrational modes of a single trapped ^{171}Yb^{+} ion. We observe an increasing phase sensitivity of the generated NOON state as the number of phonons N increases and obtain the fidelity from the contrast of the phase interference and the population of the phonon states through the two-mode projective measurement, which are significantly above the classical bound. We also measure the quantum Fisher information of the generated state and observe Heisenberg scaling in the lower bounds of phase sensitivity as N increases. Our scheme is generic and applicable to other photonic or phononic systems such as circuit QED systems or nanomechanical oscillators, which have Jaynes-Cummings-type of interactions.
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Affiliation(s)
- Junhua Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, People's Republic of China
- Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, People's Republic of China
| | - Mark Um
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
| | - Dingshun Lv
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
| | - Jing-Ning Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
| | - Lu-Ming Duan
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
| | - Kihwan Kim
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing, 100084, People's Republic of China
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17
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Ding S, Maslennikov G, Hablützel R, Matsukevich D. Quantum Simulation with a Trilinear Hamiltonian. PHYSICAL REVIEW LETTERS 2018; 121:130502. [PMID: 30312083 DOI: 10.1103/physrevlett.121.130502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2018] [Revised: 08/12/2018] [Indexed: 06/08/2023]
Abstract
Interaction among harmonic oscillators described by a trilinear Hamiltonian ℏξ(a^{†}bc+ab^{†}c^{†}) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coulomb potential in a linear trapped three-ion crystal, we experimentally implement it among three normal modes of motion in the strong-coupling regime, where the coupling strength is much larger than the decoherence rate of the ion motion. We use it to simulate the interaction of an atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down-conversion in the regime of a depleted pump.
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Affiliation(s)
- Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
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18
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Ding S, Maslennikov G, Hablützel R, Matsukevich D. Cross-Kerr Nonlinearity for Phonon Counting. PHYSICAL REVIEW LETTERS 2017; 119:193602. [PMID: 29219528 DOI: 10.1103/physrevlett.119.193602] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2017] [Indexed: 06/07/2023]
Abstract
State measurement of a quantum harmonic oscillator is essential in quantum optics and quantum information processing. In a system of trapped ions, we experimentally demonstrate the projective measurement of the state of the ions' motional mode via an effective cross-Kerr coupling to another motional mode. This coupling is induced by the intrinsic nonlinearity of the Coulomb interaction between the ions. We spectroscopically resolve the frequency shift of the motional sideband of the first mode due to the presence of single phonons in the second mode and use it to reconstruct the phonon number distribution of the second mode.
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Affiliation(s)
- Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551 Singapore, Singapore
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