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Kirsten-Siemß JN, Fitzek F, Schubert C, Rasel EM, Gaaloul N, Hammerer K. Large-Momentum-Transfer Atom Interferometers with μrad-Accuracy Using Bragg Diffraction. PHYSICAL REVIEW LETTERS 2023; 131:033602. [PMID: 37540849 DOI: 10.1103/physrevlett.131.033602] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Revised: 02/20/2023] [Accepted: 05/25/2023] [Indexed: 08/06/2023]
Abstract
Large-momentum-transfer (LMT) atom interferometers using elastic Bragg scattering on light waves are among the most precise quantum sensors to date. To advance their accuracy from the mrad to the μrad regime, it is necessary to understand the rich phenomenology of the Bragg interferometer, which differs significantly from that of a standard two-mode interferometer. We develop an analytic model for the interferometer signal and demonstrate its accuracy using comprehensive numerical simulations. Our analytic treatment allows the determination of the atomic projection noise limit of a LMT Bragg interferometer and provides the means to saturate this limit. It affords accurate knowledge of the systematic phase errors as well as their suppression by 2 orders of magnitude down to a few μrad using appropriate light-pulse parameters.
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Affiliation(s)
- J-N Kirsten-Siemß
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, D-30167 Hannover, Germany
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - F Fitzek
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, D-30167 Hannover, Germany
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - C Schubert
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, Callinstraße 30b, D-30167 Hannover, Germany
| | - E M Rasel
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - N Gaaloul
- Leibniz Universität Hannover, Institut für Quantenoptik, Welfengarten 1, D-30167 Hannover, Germany
| | - K Hammerer
- Leibniz Universität Hannover, Institut für Theoretische Physik, Appelstraße 2, D-30167 Hannover, Germany
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Fu L, Lin M, Liang Z, Wang Q, Zheng Y, Ouyang Z. The Transmission Properties of One-Dimensional Photonic Crystals with Gradient Materials. MATERIALS (BASEL, SWITZERLAND) 2022; 15:8049. [PMID: 36431534 PMCID: PMC9695922 DOI: 10.3390/ma15228049] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 11/08/2022] [Accepted: 11/11/2022] [Indexed: 06/16/2023]
Abstract
In this paper, we studied the transmission properties, including photonic band gap (PBG) and defect mode properties, of one-dimensional photonic crystals (1D PCs) consisting of gradient materials. When keeping the average refractive index of the gradient materials in the 1D gradient-material PCs (1D GPCs) the same as the index of the corresponding normal materials in the 1D normal-material PCs (1D NPCs), by transfer matrix method, we found that the complete 1D GPCs with high-index gradient materials benefit to achieve larger omni-PBG than that in 1D NPCs. In our high-index gradient material case, for TE(TM) wave, the optimal omni-PBGs in 1D GPCs with first- and second-order gradient materials are 38.6% (50.2%) and 15.9% (22.3%) larger than that in 1D NPCs; while for the optimal relative bandwidths of omni-PBG, the corresponding promotions are 41.1% (52.3%) and 16.1% (22.6%), respectively. In addition, when defective 1D GPCs have gradient-material defect, the position of defect modes can be adjusted by selecting proper parameters of the gradient materials. These types of research are useful for designing wide PBG devices and tunable narrow-band filters which have potential application in optical communication.
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Affiliation(s)
- Lixin Fu
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Mi Lin
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Zixian Liang
- College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
| | - Qiong Wang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Yaoxian Zheng
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
| | - Zhengbiao Ouyang
- Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
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Fitzek F, Siemß JN, Seckmeyer S, Ahlers H, Rasel EM, Hammerer K, Gaaloul N. Universal atom interferometer simulation of elastic scattering processes. Sci Rep 2020; 10:22120. [PMID: 33335161 PMCID: PMC7746744 DOI: 10.1038/s41598-020-78859-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2020] [Accepted: 11/30/2020] [Indexed: 11/09/2022] Open
Abstract
In this article, we introduce a universal simulation framework covering all regimes of matter-wave light-pulse elastic scattering. Applied to atom interferometry as a study case, this simulator solves the atom-light diffraction problem in the elastic case, i.e., when the internal state of the atoms remains unchanged. Taking this perspective, the light-pulse beam splitting is interpreted as a space and time-dependent external potential. In a shift from the usual approach based on a system of momentum-space ordinary differential equations, our position-space treatment is flexible and scales favourably for realistic cases where the light fields have an arbitrary complex spatial behaviour rather than being mere plane waves. Moreover, the solver architecture we developed is effortlessly extended to the problem class of trapped and interacting geometries, which has no simple formulation in the usual framework of momentum-space ordinary differential equations. We check the validity of our model by revisiting several case studies relevant to the precision atom interferometry community. We retrieve analytical solutions when they exist and extend the analysis to more complex parameter ranges in a cross-regime fashion. The flexibility of the approach, the insight it gives, its numerical scalability and accuracy make it an exquisite tool to design, understand and quantitatively analyse metrology-oriented matter-wave interferometry experiments.
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Affiliation(s)
- Florian Fitzek
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany.,Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Jan-Niclas Siemß
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany.,Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Stefan Seckmeyer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Holger Ahlers
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Ernst M Rasel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany
| | - Klemens Hammerer
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Naceur Gaaloul
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany.
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Chen C, Ivory M, Aubin S, Delos JB. Dynamical monodromy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012919. [PMID: 24580309 DOI: 10.1103/physreve.89.012919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2013] [Indexed: 06/03/2023]
Abstract
Integrable Hamiltonian systems are said to display nontrivial monodromy if fundamental action-angle loops defined on phase-space tori change their topological structure when the system is carried around a circuit. In an earlier paper it was shown that this topological change can occur as a result of time evolution under certain rather abstract flows in phase space. In the present paper, we show that the same topological change can occur as a result of application of ordinary forces. We also show how this dynamical phenomenon could be observed experimentally in classical or in quantum systems.
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Affiliation(s)
- C Chen
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - M Ivory
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - S Aubin
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
| | - J B Delos
- Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
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Chiow SW, Herrmann S, Chu S, Müller H. Noise-immune conjugate large-area atom interferometers. PHYSICAL REVIEW LETTERS 2009; 103:050402. [PMID: 19792468 DOI: 10.1103/physrevlett.103.050402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2009] [Indexed: 05/28/2023]
Abstract
We present a pair of simultaneous conjugate Ramsey-Bordé atom interferometers using large (20variant Planck's over 2pik)-momentum transfer beam splitters, where variant Planck's over 2pik is the photon momentum. Simultaneous operation allows for common-mode rejection of vibrational noise. This allows us to surpass the enclosed space-time area of previous interferometers with a splitting of 20variant Planck's over 2pik by a factor of 2500. Using a splitting of 10variant Planck's over 2pik, we demonstrate a 3.4 ppb resolution in the measurement of the fine structure constant. Examples for applications in tests of fundamental laws of physics are given.
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Affiliation(s)
- Sheng-Wey Chiow
- Physics Department, Stanford University, Stanford, California 94305, USA
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Hughes KJ, Burke JHT, Sackett CA. Suspension of atoms using optical pulses, and application to gravimetry. PHYSICAL REVIEW LETTERS 2009; 102:150403. [PMID: 19518607 DOI: 10.1103/physrevlett.102.150403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2008] [Indexed: 05/27/2023]
Abstract
Atoms from a (87)Rb condensate are suspended against gravity using repeated reflections from a pulsed optical standing wave. Up to 100 reflections are observed, yielding suspension times of over 100 ms. The local gravitational acceleration can be determined from the pulse rate required to achieve suspension. Further, a gravitationally sensitive atom interferometer was implemented using the suspended atoms. This technique could potentially provide a precision measurement of gravity without requiring the atoms to fall a large distance.
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Affiliation(s)
- K J Hughes
- Physics Department, University of Virginia, Charlottesville, Virginia 22904, USA
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Müller H, Chiow SW, Long Q, Herrmann S, Chu S. Atom interferometry with up to 24-photon-momentum-transfer beam splitters. PHYSICAL REVIEW LETTERS 2008; 100:180405. [PMID: 18518355 DOI: 10.1103/physrevlett.100.180405] [Citation(s) in RCA: 55] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2007] [Indexed: 05/26/2023]
Abstract
We present up to 24-photon Bragg diffraction as a beam splitter in light-pulse atom interferometers to achieve the largest splitting in momentum space so far. Relative to the 2-photon processes used in the most sensitive present interferometers, these large momentum transfer beam splitters increase the phase shift 12-fold for Mach-Zehnder (MZ) and 144-fold for Ramsey-Bordé (RB) geometries. We achieve a high visibility of the interference fringes (up to 52% for MZ or 36% for RB) and long pulse separation times that are possible only in atomic fountain setups. As the atom's internal state is not changed, important systematic effects can cancel.
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Affiliation(s)
- Holger Müller
- Physics Department, Stanford University, 382 Via Pueblo Mall, Stanford, California 94305, USA
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Steck DA, Oskay WH, Raizen MG. Fluctuations and decoherence in chaos-assisted tunneling. PHYSICAL REVIEW LETTERS 2002; 88:120406. [PMID: 11909436 DOI: 10.1103/physrevlett.88.120406] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2001] [Indexed: 05/23/2023]
Abstract
We study quantum dynamical tunneling between two symmetry-related islands of stability in the phase space of a classically chaotic system. The setting for these experiments is the motion of carefully prepared samples of cesium atoms in an amplitude-modulated standing wave of light. We examine the dependence of the tunneling dynamics on the system parameters and indicate how the observed features provide evidence for chaos-assisted (three-state) tunneling. We also observe the influence of a noisy perturbation of the standing-wave intensity, which destroys the tunneling oscillations, and we show that the tunneling is more sensitive to the noise for a smaller value of the effective Planck constant.
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Affiliation(s)
- Daniel A Steck
- Department of Physics and Center for Nonlinear Dynamics, The University of Texas at Austin, Austin, Texas 78712-1081, USA
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Steck DA, Oskay WH, Raizen MG. Observation of chaos-assisted tunneling between islands of stability. Science 2001; 293:274-8. [PMID: 11441148 DOI: 10.1126/science.1061569] [Citation(s) in RCA: 123] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
We report the direct observation of quantum dynamical tunneling of atoms between separated momentum regions in phase space. We study how the tunneling oscillations are affected as a quantum symmetry is broken and as the initial atomic state is changed. We also provide evidence that the tunneling rate is greatly enhanced by the presence of chaos in the classical dynamics. This tunneling phenomenon represents a dramatic manifestation of underlying classical chaos in a quantum system.
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Affiliation(s)
- D A Steck
- Department of Physics, The University of Texas at Austin, Austin, TX 78712-1081, USA
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Houde O, Kadio D, Pruvost L. Cold atom beam splitter realized with two crossing dipole guides. PHYSICAL REVIEW LETTERS 2000; 85:5543-5546. [PMID: 11136042 DOI: 10.1103/physrevlett.85.5543] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2000] [Indexed: 05/23/2023]
Abstract
Cold rubidium atoms, coupled and guided in a vertical laser beam by the dipole force, have been split into two atomic beams, by using a second time-dependent laser beam crossing the vertical one at a 0.12 rad angle. Transfer efficiency as large as 40% has been obtained. At 10 mm below the cold atom source, the two atomic beams have a few hundred micron size and are more than one millimeter apart from each other.
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Affiliation(s)
- O Houde
- Laboratoire Aimé Cotton, CNRS II, bâtiment 505, Campus d'Orsay, 91405 Orsay cedex, France
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Dürr S, Kunze S, Rempe G. Pendellösung oscillations in second-order Bragg scattering of atoms from a standing light wave. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/1355-5111/8/3/016] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Bernet S, Oberthaler MK, Abfalterer R, Schmiedmayer J, Zeilinger A. Coherent Frequency Shift of Atomic Matter Waves. PHYSICAL REVIEW LETTERS 1996; 77:5160-5163. [PMID: 10062731 DOI: 10.1103/physrevlett.77.5160] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Anderson BB, Brodsky AM, Burgess LW. Threshold effects in light scattering from a binary diffraction grating. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:912-923. [PMID: 9965139 DOI: 10.1103/physreve.54.912] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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