1
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Paul S, Kannan JB, Santhanam MS. Interaction-induced directed transport in quantum chaotic subsystems. Phys Rev E 2023; 108:044208. [PMID: 37978627 DOI: 10.1103/physreve.108.044208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
Quantum directed transport can be realized in noninteracting, deterministic, chaotic systems by appropriately breaking the spatiotemporal symmetries in the potential. In this work, the focus is on the class of interacting two-body quantum systems whose classical limit is chaotic. It is shown that one subsystem effectively acts as a source of "noise" to the other leading to intrinsic temporal symmetry breaking. Then, the quantum directed currents, even if prohibited by symmetries in the composite system, can be realized in the subsystems. This current is of quantum origin and does not arise from semiclassical effects. This protocol provides a minimal framework-broken spatial symmetry in the potential and presence of interactions-for realizing directed transport in interacting chaotic systems. It is also shown that the magnitude of directed current undergoes multiple current reversals upon varying the interaction strength and this allows for controlling the currents. It is explicitly demonstrated in the two-body interacting kicked rotor model. The interaction-induced mechanism for subsystem directed currents would be applicable to other interacting quantum systems as well.
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Affiliation(s)
- Sanku Paul
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824 USA
| | - J Bharathi Kannan
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
| | - M S Santhanam
- Department of Physics, Indian Institute of Science Education and Research, Pune 411008, India
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2
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Devolder A, Tscherbul TV, Brumer P. Coherent Control of Ultracold Molecular Collisions: The Role of Resonances. J Phys Chem Lett 2023; 14:2171-2177. [PMID: 36808981 DOI: 10.1021/acs.jpclett.3c00146] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates related to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.
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Affiliation(s)
- Adrien Devolder
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Timur V Tscherbul
- Department of Physics, University of Nevada, Reno, Nevada 89557, United States of America
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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3
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Arranz FJ, Benito RM, Borondo F. Shannon entropy at avoided crossings in the quantum transition from order to chaos. Phys Rev E 2019; 99:062209. [PMID: 31330703 DOI: 10.1103/physreve.99.062209] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2019] [Indexed: 11/06/2022]
Abstract
Shannon entropy is studied for the series of avoided crossings that characterize the transition from order to chaos in quantum mechanics. In order to be able to study jointly this entropy for discrete and continuous probability, calculations have been performed on a quantized map, the kicked Harper map, resulting in a different behavior, as order-chaos transition takes place, for the discrete (position representation) and continuous (coherent state representation) cases. This different behavior is analyzed in terms of the distribution of zeros of the Husimi function.
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Affiliation(s)
- F J Arranz
- Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, av. Puerta de Hierro 2-4, 28040 Madrid, Spain
| | - R M Benito
- Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, av. Puerta de Hierro 2-4, 28040 Madrid, Spain
| | - F Borondo
- Instituto de Ciencias Matemáticas (ICMAT), Cantoblanco, 28049 Madrid, Spain.,Departamento de Química, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
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4
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Zhao WL, Wang J, Wang X, Tong P. Directed momentum current induced by the PT-symmetric driving. Phys Rev E 2019; 99:042201. [PMID: 31108677 DOI: 10.1103/physreve.99.042201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2018] [Indexed: 06/09/2023]
Abstract
We investigate the directed momentum current in the quantum kicked rotor model with PT-symmetric deriving potential. For the quantum nonresonance case, the values of quasienergy become complex when the strength of the imaginary part of the kicking potential exceeds a threshold value, which demonstrates the appearance of the spontaneous PT symmetry breaking. In the vicinity of the transition point, the momentum current exhibits a staircase growth with time. Each platform of the momentum current corresponds to the mean momentum of some eigenstates of the Floquet operator whose imaginary parts of the quasienergy are significantly large. Above the transition point, the momentum current increases linearly with time. Interestingly, its acceleration rate exhibits a kind of "quantized" increment with the kicking strength. We propose a modified classical acceleration mode of the kicked rotor model to explain such an intriguing phenomenon. Our theoretical prediction is in good agreement with numerical results.
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Affiliation(s)
- Wen-Lei Zhao
- School of Science, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Jiaozi Wang
- Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiaohui Wang
- School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
| | - Peiqing Tong
- Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China
- Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing, Jiangsu 210023, China
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5
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Grossert C, Leder M, Denisov S, Hänggi P, Weitz M. Experimental control of transport resonances in a coherent quantum rocking ratchet. Nat Commun 2016; 7:10440. [PMID: 26852803 PMCID: PMC4748114 DOI: 10.1038/ncomms10440] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2015] [Accepted: 12/10/2015] [Indexed: 01/04/2023] Open
Abstract
The ratchet phenomenon is a means to get directed transport without net forces. Originally conceived to rectify stochastic motion and describe operational principles of biological motors, the ratchet effect can be used to achieve controllable coherent quantum transport. This transport is an ingredient of several perspective quantum devices including atomic chips. Here we examine coherent transport of ultra-cold atoms in a rocking quantum ratchet. This is realized by loading a rubidium atomic Bose–Einstein condensate into a periodic optical potential subjected to a biharmonic temporal drive. The achieved long-time coherence allows us to resolve resonance enhancement of the atom transport induced by avoided crossings in the Floquet spectrum of the system. By tuning the strength of the temporal modulations, we observe a bifurcation of a single resonance into a doublet. Our measurements reveal the role of interactions among Floquet eigenstates for quantum ratchet transport. The ratchet effect can be used as a tool to control coherent quantum transport of ultra-cold atoms. Here, the authors demonstrate a rocking quantum ratchet with a rubidium BEC, and reveal the existence of quantum transport resonances.
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Affiliation(s)
- Christopher Grossert
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Martin Leder
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
| | - Sergey Denisov
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Sumy State University, Rimsky-Korsakov Street 2, 40007 Sumy, Ukraine
| | - Peter Hänggi
- Department of Applied Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia.,Institut für Physik, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany.,Nanosystems Initiative Munich, Schellingstr. 4, D-80799 München, Germany
| | - Martin Weitz
- Institut für Angewandte Physik der Universität Bonn, Wegelerstr. 8, 53115 Bonn, Germany
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6
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7
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Abstract
This paper is a brief review of classical and quantum transport phenomena, as well as related spectral properties, exhibited by one-dimensional periodically kicked systems. Two representative and fundamentally different classes of systems will be considered: those satisfying the classical Kolmogorov−Arnol’d−Moser scenario and those that do not. The experimental realization of some of these systems using atom-optics methods will be mentioned.
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Affiliation(s)
- Itzhack Dana
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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8
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Wulf T, Liebchen B, Schmelcher P. Disorder induced regular dynamics in oscillating lattices. PHYSICAL REVIEW LETTERS 2014; 112:034101. [PMID: 24484140 DOI: 10.1103/physrevlett.112.034101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2013] [Indexed: 06/03/2023]
Abstract
We explore the impact of weak disorder on the dynamics of classical particles in a periodically oscillating lattice. It is demonstrated that the disorder induces a hopping process from diffusive to regular motion; i.e., we observe the counterintuitive phenomenon that disorder leads to regular behavior. If the disorder is localized in a finite-sized part of the lattice, the described hopping causes initially diffusive particles to even accumulate in regular structures of the corresponding phase space. A hallmark of this accumulation is the emergence of pronounced peaks in the velocity distribution of particles that should be detectable in state of the art experiments, e.g., with cold atoms in optical lattices.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Benno Liebchen
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Peter Schmelcher
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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9
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Ho DYH, Gong J. Quantized adiabatic transport in momentum space. PHYSICAL REVIEW LETTERS 2012; 109:010601. [PMID: 23031095 DOI: 10.1103/physrevlett.109.010601] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2012] [Indexed: 06/01/2023]
Abstract
Though topological aspects of energy bands are known to play a key role in quantum transport in solid-state systems, the implications of Floquet band topology for transport in momentum space (i.e., acceleration) have not been explored so far. Using a ratchet accelerator model inspired by existing cold-atom experiments, here we characterize a class of extended Floquet bands of one-dimensional driven quantum systems by Chern numbers, reveal topological phase transitions therein, and theoretically predict the quantization of adiabatic transport in momentum space. Numerical results confirm our theory and indicate the feasibility of experimental studies.
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Affiliation(s)
- Derek Y H Ho
- Department of Physics and Center for Computational Science and Engineering, National University of Singapore, 117542, Singapore
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10
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Wulf T, Petri C, Liebchen B, Schmelcher P. Analysis of interface conversion processes of ballistic and diffusive motion in driven superlattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:016201. [PMID: 23005501 DOI: 10.1103/physreve.86.016201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2012] [Revised: 06/13/2012] [Indexed: 06/01/2023]
Abstract
We explore the nonequilibrium dynamics of noninteracting classical particles in a one-dimensional driven superlattice which is composed of domains exposed to different time-dependent forces. It is shown how the combination of directed transport and conversion processes from diffusive to ballistic motion causes strong correlations between velocity and phase for particles passing through a superlattice. A detailed understanding of the underlying mechanism allows us to tune the resulting velocity distributions at distinguished points in the superlattice by means of local variations of the applied driving force. As an intriguing application we present a scheme how initially diffusive particles can be transformed into a monoenergetic pulsed particle beam whose parameters such as its energy can be varied.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
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11
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Dana I, Roitberg VB. Weak-chaos ratchet accelerator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066213. [PMID: 21797467 DOI: 10.1103/physreve.83.066213] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Indexed: 05/31/2023]
Abstract
Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.
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Affiliation(s)
- Itzhack Dana
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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12
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Pal H, Santhanam MS. Dynamics of kicked particles in a double-barrier structure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056212. [PMID: 21230568 DOI: 10.1103/physreve.82.056212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2010] [Indexed: 05/30/2023]
Abstract
We study the classical and quantum dynamics of periodically kicked particles placed initially within an open double-barrier structure. This system does not obey the Kolmogorov-Arnold-Moser (KAM) theorem and displays chaotic dynamics. The phase-space features induced by non-KAM nature of the system lead to dynamical features such as the nonequilibrium steady state, classically induced saturation of energy growth and momentum filtering. We also comment on the experimental feasibility of this system as well as its relevance in the context of current interest in classically induced localization and chaotic ratchets.
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Affiliation(s)
- Harinder Pal
- Physical Research Laboratory, Navrangpura, Ahmedabad 380009, India.
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13
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Ghosh P, Shit A, Chattopadhyay S, Chaudhuri JR. Realization of a Brownian engine to study transport phenomena: a semiclassical approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:061112. [PMID: 20866383 DOI: 10.1103/physreve.81.061112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2010] [Revised: 04/21/2010] [Indexed: 05/29/2023]
Abstract
Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle. We present here a self-consistent theory based on the system-reservoir coupling model, within a microscopic approach, of fluctuation induced transport in the semiclassical limit for a general system coupled with two heat baths kept at different temperatures. This essentially puts forth an approach to semiclassical state-dependent diffusion. We also explore the possibility of observing a current when the temperature of the two baths are different, and also envisage that our system may act as a Carnot engine even when the bath temperatures are the same. The condition for such a construction has been elucidated.
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Affiliation(s)
- Pradipta Ghosh
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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14
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Bandyopadhyay JN, Wang J, Gong J. Generating a fractal butterfly Floquet spectrum in a class of driven SU(2) systems: eigenstate statistics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:066212. [PMID: 20866506 DOI: 10.1103/physreve.81.066212] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2009] [Revised: 04/30/2010] [Indexed: 05/29/2023]
Abstract
The Floquet spectra of a class of driven SU(2) systems have been shown to display butterfly patterns with multifractal properties. The implication of such critical spectral behavior for the Floquet eigenstate statistics is studied in this work. Following the methodologies for understanding the fractal behavior of energy eigenstates of time-independent systems on the Anderson transition point, we analyze the distribution profile, the mean value, and the variance of the logarithm of the inverse participation ratio of the Floquet eigenstates associated with multifractal Floquet spectra. The results show that the Floquet eigenstates also display fractal behavior but with features markedly different from those in time-independent Anderson-transition models. This motivated us to propose random unitary matrix ensemble, called "power-law random banded unitary matrix" ensemble, to illuminate the Floquet eigenstate statistics of critical driven systems. The results based on the proposed random matrix model are consistent with those obtained from our dynamical examples with or without time-reversal symmetry.
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Affiliation(s)
- Jayendra N Bandyopadhyay
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore
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15
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Shit A, Chattopadhyay S, Banik SK, Chaudhuri JR. Generalized Einstein Relation in Tilted Periodic Potential: A Semiclassical Approach. J Phys Chem B 2010; 114:7854-63. [DOI: 10.1021/jp912069k] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Anindita Shit
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
| | - Sudip Chattopadhyay
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
| | - Suman Kumar Banik
- Department of Chemistry, Bose Institute, 93/1 A P C Road, Kolkata 700009, India
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16
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Petri C, Lenz F, Diakonos FK, Schmelcher P. Directed transport and localization in phase-modulated driven lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046219. [PMID: 20481819 DOI: 10.1103/physreve.81.046219] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2010] [Indexed: 05/29/2023]
Abstract
We explore the dynamics of noninteracting particles loaded into a phase-modulated one-dimensional lattice formed by laterally oscillating square barriers. Tuning the parameters of the driven unit cell of the lattice selected parts of the classical phase space can be manipulated in a controllable manner. We find superdiffusion in position space for all parameters regimes. A directed current of an ensemble of particles can be created through locally breaking the spatiotemporal symmetries of the time-driven potential. Magnitude and direction of the current are tunable. Several mechanisms for transient localization and trapping of particles in different wells of the driven unit cell are presented and analyzed.
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Affiliation(s)
- Christoph Petri
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
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17
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Dana I. Statistical approach to quantum chaotic ratchets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036210. [PMID: 20365835 DOI: 10.1103/physreve.81.036210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2009] [Indexed: 05/29/2023]
Abstract
The quantum ratchet effect in fully chaotic systems is approached by studying statistical properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical regime are those that are phase-space uniform with the maximal possible resolution of one Planck cell. General arguments in this regime, for quantum-resonance values of a scaled Planck constant variant Planck's over 2pi , predict that the distribution of the current over all such states is a zero-mean Gaussian with variance approximately Dvariant Planck's over 2pi2/(2pi2) , where D is the chaotic-diffusion coefficient. This prediction is well supported by extensive numerical evidence. The average strength of the effect, measured by the variance above, is significantly larger than that for the usual momentum states and other states. Such strong effects should be experimentally observable.
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Affiliation(s)
- Itzhack Dana
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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18
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Creffield CE, Sols F. Coherent ratchets in driven Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2009; 103:200601. [PMID: 20365971 DOI: 10.1103/physrevlett.103.200601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2009] [Revised: 10/29/2009] [Indexed: 05/29/2023]
Abstract
We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior, and space and time symmetries must both be broken to produce a current. For strong driving, the behavior becomes chaotic and the resulting effective irreversibility means that it is unnecessary to explicitly break time symmetry. Spatial asymmetry alone is then sufficient to produce the ratchet effect, even in the absence of interactions, and although the system remains completely coherent.
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Affiliation(s)
- C E Creffield
- Departamento de Física de Materiales, Universidad Complutense de Madrid, E-28040, Madrid, Spain
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Pelc J, Gong J, Brumer P. Chaos and correspondence in classical and quantum Hamiltonian ratchets: a Heisenberg approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:066207. [PMID: 19658583 DOI: 10.1103/physreve.79.066207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2008] [Indexed: 05/28/2023]
Abstract
Previous work [Gong and Brumer, Phys. Rev. Lett. 97, 240602 (2006)] motivates this study as to how asymmetry-driven quantum ratchet effects can persist despite a corresponding fully chaotic classical phase space. A simple perspective of ratchet dynamics, based on the Heisenberg picture, is introduced. We show that ratchet effects are in principle of common origin in classical and quantum mechanics, although full chaos suppresses these effects in the former but not necessarily the latter. The relationship between ratchet effects and coherent dynamical control is noted.
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Affiliation(s)
- Jordan Pelc
- Chemical Physics Theory Group, Department of Chemistry, and Centre for Quantum Information and Quantum Control, University of Toronto, Toronto, Canada M5S 3H6
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20
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Wang J, Gong J. Quantum ratchet accelerator without a bichromatic lattice potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036219. [PMID: 18851133 DOI: 10.1103/physreve.78.036219] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2008] [Indexed: 05/26/2023]
Abstract
In a quantum ratchet accelerator system, a linearly increasing directed current can be dynamically generated without using a biased field. Generic quantum ratchet acceleration with full classical chaos [J. B. Gong and P. Brumer, Phys. Rev. Lett. 97, 240602 (2006)] constitutes a new element of quantum chaos and an interesting violation of a sum rule of classical ratchet transport. Here we propose a simple quantum ratchet accelerator model that can also generate linearly increasing quantum current with full classical chaos. This model does not require a bichromatic lattice potential. It is based on a variant of an on-resonance kicked-rotor system, periodically kicked by two optical lattice potentials of the same lattice constant, but with unequal amplitudes and a fixed phase shift between them. The dependence of the ratchet current acceleration rate on the system parameters is studied in detail. The cold-atom version of our quantum ratchet accelerator model should be realizable by introducing slight modifications to current cold-atom experiments.
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Affiliation(s)
- Jiao Wang
- Temasek Laboratories, National University of Singapore, 117542, Singapore
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21
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Bhattacharya S, Chaudhury P, Chattopadhyay S, Chaudhuri JR. Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:021123. [PMID: 18850802 DOI: 10.1103/physreve.78.021123] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2008] [Indexed: 05/26/2023]
Abstract
A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.
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Affiliation(s)
- Satyabrata Bhattacharya
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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22
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Kudo K, Monteiro TS. Quantum transport and spin dynamics on shearless tori. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:055203. [PMID: 18643121 DOI: 10.1103/physreve.77.055203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2008] [Indexed: 05/26/2023]
Abstract
We investigate quantum dynamics in phase-space regions containing "shearless tori." We show that the properties of these peculiar classical phase-space structures-important to the dynamics of tokamaks-may be exploited for quantum information applications. In particular we show that shearless tori permit the nondispersive transmission of localized wave packets. The quantum many-body Hamiltonian of a Heisenberg ferromagnetic spin chain, subjected to an oscillating magnetic field, can be reduced to a classical one-body "image" dynamical system which is the well-studied Harper map. The Harper map belongs to a class of Hamiltonian systems (nontwist maps) which contain shearless tori. We show that a variant with sinusoidal time driving "driven Harper model" produces shearless tori which are especially suitable for quantum state transfer. The behavior of the concurrence is investigated as an example.
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Affiliation(s)
- K Kudo
- Department of Applied Physics, Graduate School of Engineering, Osaka City University, Osaka 558-8585, Japan.
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Kenfack A, Gong J, Pattanayak AK. Controlling the ratchet effect for cold atoms. PHYSICAL REVIEW LETTERS 2008; 100:044104. [PMID: 18352279 DOI: 10.1103/physrevlett.100.044104] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2007] [Indexed: 05/26/2023]
Abstract
Low-order quantum resonances manifested by directed currents have been realized with cold atoms. Here we show that by increasing the strength of an experimentally achievable delta-kicking ratchet potential, quantum resonances of a very high order may naturally emerge and can induce larger ratchet currents than low-order resonances, with the underlying classical limit being fully chaotic. The results offer a means of controlling quantum transport of cold atoms.
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Affiliation(s)
- Anatole Kenfack
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
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24
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Dana I, Ramareddy V, Talukdar I, Summy GS. Experimental realization of quantum-resonance ratchets at arbitrary quasimomenta. PHYSICAL REVIEW LETTERS 2008; 100:024103. [PMID: 18232872 DOI: 10.1103/physrevlett.100.024103] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2007] [Revised: 08/30/2007] [Indexed: 05/25/2023]
Abstract
Quantum-resonance ratchets associated with the kicked particle are experimentally realized for arbitrary quasimomentum using a Bose-Einstein condensate (BEC) exposed to a pulsed standing light wave. The ratchet effect for general quasimomentum arises even though both the standing-wave potential and the initial state of the BEC have a point symmetry. The experimental results agree well with theoretical ones which take into account the finite quasimomentum width of the BEC. In particular, this width is shown to cause a suppression of the ratchet acceleration for exactly resonant quasimomentum, leading to a saturation of the directed current.
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Affiliation(s)
- I Dana
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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25
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Ermann L, Carlo GG, Saraceno M. Transport phenomena in the asymmetric quantum multibaker map. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:011126. [PMID: 18351837 DOI: 10.1103/physreve.77.011126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2007] [Indexed: 05/26/2023]
Abstract
By studying a modified (unbiased) quantum multibaker map, we were able to obtain a finite asymptotic quantum current without a classical analog. This result suggests a general method for the design of purely quantum ratchets and sheds light on the investigation of the mechanisms leading to net transport generation by breaking symmetries of quantum systems. Moreover, we propose the multibaker map as a resource to study directed transport phenomena in chaotic systems without bias. In fact, this is a paradigmatic model in classical and quantum chaos, but also in statistical mechanics.
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Affiliation(s)
- Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
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26
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Gong J, Wang J. Quantum diffusion dynamics in nonlinear systems: a modified kicked-rotor model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:036217. [PMID: 17930333 DOI: 10.1103/physreve.76.036217] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2007] [Indexed: 05/25/2023]
Abstract
Using a simple method analogous to a quantum rephasing technique, a simple modification to a paradigm of classical and quantum chaos is proposed. The interesting quantum maps thus obtained display remarkably rich quantum dynamics. Emphasis is placed on the destruction of dynamical localization without breaking periodicity, unbounded quantum anomalous diffusion in integrable systems, and transient dynamical localization. Experimental realizations of this work are also discussed.
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Affiliation(s)
- Jiangbin Gong
- Department of Physics and Centre of Computational Science and Engineering, National University of Singapore, 117542, Singapore
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27
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Sadgrove M, Horikoshi M, Sekimura T, Nakagawa K. Rectified momentum transport for a kicked Bose-Einstein condensate. PHYSICAL REVIEW LETTERS 2007; 99:043002. [PMID: 17678359 DOI: 10.1103/physrevlett.99.043002] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2007] [Indexed: 05/16/2023]
Abstract
We report the experimental observation of rectified momentum transport for a Bose-Einstein condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and -2hkl momentum states using an optical pi/2 pulse. By changing the relative phase of the superposed states, a momentum current in either direction along the standing wave may be produced. We offer an interpretation based on matter-wave interference, showing that the observed effect is uniquely quantum.
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Affiliation(s)
- Mark Sadgrove
- Institute for Laser Science, The University of Electro Communications, Chofushi, Chofugaoka 1-5-1, Japan.
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28
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Dana I, Roitberg V. Quantum resonances and ratchets in free-falling frames. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:015201. [PMID: 17677524 DOI: 10.1103/physreve.76.015201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2007] [Indexed: 05/16/2023]
Abstract
Quantum resonance (QR) is defined in the free-falling frame of the quantum kicked particle subjected to gravity. The general QR conditions are derived. They imply the rationality of the gravity parameter eta , the kicking-period parameter tau/(2pi) , and the quasimomentum beta . Exact results are obtained concerning wave-packet evolution for arbitrary periodic kicking potentials in the case of integer tau/(2pi) (the main QRs). It is shown that a quantum ratchet generally arises in this case for resonant beta . The noninertial nature of the free-falling frame affects the ratchet by effectively changing the kicking potential to one depending on (beta,eta) . For a simple class of initial wave packets, it is explicitly shown that the ratchet characteristics are determined to a large extent by symmetry properties and by number-theoretical features of eta .
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Affiliation(s)
- Itzhack Dana
- Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
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29
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Jones PH, Goonasekera M, Meacher DR, Jonckheere T, Monteiro TS. Directed motion for delta-kicked atoms with broken symmetries: comparison between theory and experiment. PHYSICAL REVIEW LETTERS 2007; 98:073002. [PMID: 17359021 DOI: 10.1103/physrevlett.98.073002] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2006] [Indexed: 05/14/2023]
Abstract
We report an experimental investigation of momentum diffusion in the delta-function kicked rotor where time symmetry is broken by a two-period kicking cycle and spatial symmetry by an alternating linear potential. We exploit this, and a technique involving a moving optical potential, to create an asymmetry in the momentum diffusion that is due to the classical chaotic diffusion. This represents a realization of a type of Hamiltonian quantum ratchet.
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Affiliation(s)
- P H Jones
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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