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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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Cubero D. Brillouin propagation modes of cold atoms undergoing Sisyphus cooling. Phys Rev E 2023; 107:034102. [PMID: 37072942 DOI: 10.1103/physreve.107.034102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2022] [Accepted: 02/13/2023] [Indexed: 04/20/2023]
Abstract
An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equations for the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.
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Affiliation(s)
- David Cubero
- Departamento de Física Aplicada I, Escuela Politécnica Superior, Universidad de Sevilla, Calle Virgen de África 7, 41011 Sevilla, Spain
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3
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Chen R, Jiang L. Directed transport of symmetrically periodic system induced by "color" breaking of noise. CHAOS (WOODBURY, N.Y.) 2020; 30:123140. [PMID: 33380021 DOI: 10.1063/5.0031756] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 12/04/2020] [Indexed: 06/12/2023]
Abstract
In general, no transport can emerge in a spatially symmetric periodic system subjected to an unbiased dichotomous periodic driving. Here, we used a noise, which switches synchronously with the driving in three cases [switch between Gaussian white noise and colored noise, two colored noises with different colors (e.g., autocorrelation rate), and Gaussian white noise and harmonic velocity noise], to drive such a symmetric system. Numerical results for the cases indicate that the directed transport of the symmetric system can be induced merely by the color breaking (the difference in two autocorrelation rates) of the switch noise. The amplitude of current depends on the difference, i.e., the greater the difference, the greater the current. Also, the greater autocorrelation rate between the two noises determines the direction of current. The current as a function of the noise intensity for all cases has in common that appropriate noise intensity induces optimal transport. Further investigations show that the color breaking comes from the difference of barrier heights between the left and right-tilted potentials induced by the different autocorrelation rates.
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Affiliation(s)
- Ruyin Chen
- School of Ophthalmology and Optometry and Eye Hospital, Wenzhou Medical University, Wenzhou 325000, China
| | - Luoluo Jiang
- School of Information Management and Artificial, Zhejiang University of Finance and Economics, Hangzhou 310018, China
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Paul S, Santhanam MS. Floquet states of a kicked particle in a singular potential: Exponential and power-law profiles. Phys Rev E 2018; 97:032217. [PMID: 29776057 DOI: 10.1103/physreve.97.032217] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2017] [Indexed: 11/06/2022]
Abstract
It is well known that, in the chaotic regime, all the Floquet states of kicked rotor system display an exponential profile resulting from dynamical localization. If the kicked rotor is placed in an additional stationary infinite potential well, its Floquet states display power-law profile. It has also been suggested in general that the Floquet states of periodically kicked systems with singularities in the potential would have power-law profile. In this work, we study the Floquet states of a kicked particle in finite potential barrier. By varying the height of finite potential barrier, the nature of transition in the Floquet state from exponential to power-law decay profile is studied. We map this system to a tight-binding model and show that the nature of decay profile depends on energy band spanned by the Floquet states (in unperturbed basis) relative to the potential height. This property can also be inferred from the statistics of Floquet eigenvalues and eigenvectors. This leads to an unusual scenario in which the level spacing distribution, as a window in to the spectral correlations, is not a unique characteristic for the entire system.
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Affiliation(s)
- Sanku Paul
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - M S Santhanam
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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5
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Carlo GG, Ermann L, Rivas AMF, Spina ME. Signatures of classical structures in the leading eigenstates of quantum dissipative systems. Phys Rev E 2017; 96:032202. [PMID: 29346928 DOI: 10.1103/physreve.96.032202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2017] [Indexed: 06/07/2023]
Abstract
By analyzing a paradigmatic example of the theory of dissipative systems-the classical and quantum dissipative standard map-we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kinds of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Alejandro M F Rivas
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - María E Spina
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
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6
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Carlo GG, Ermann L, Rivas AMF, Spina ME, Poletti D. Classical counterparts of quantum attractors in generic dissipative systems. Phys Rev E 2017; 95:062202. [PMID: 28709295 DOI: 10.1103/physreve.95.062202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Indexed: 11/07/2022]
Abstract
In the context of dissipative systems, we show that for any quantum chaotic attractor a corresponding classical chaotic attractor can always be found. We provide a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In cases where an approximate pointlike quantum distribution is found, it can be associated with exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behavior can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant ℏ_{eff}. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Alejandro M F Rivas
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - María E Spina
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Dario Poletti
- Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore
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Sadgrove M, Wimberger S, Nic Chormaic S. Quantum coherent tractor beam effect for atoms trapped near a nanowaveguide. Sci Rep 2016; 6:28905. [PMID: 27440516 PMCID: PMC4954976 DOI: 10.1038/srep28905] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2016] [Accepted: 06/10/2016] [Indexed: 11/25/2022] Open
Abstract
We propose several schemes to realize a tractor beam effect for ultracold atoms in the vicinity of a few-mode nanowaveguide. Atoms trapped near the waveguide are transported in a direction opposite to the guided mode propagation direction. We analyse three specific examples for ultracold (23)Na atoms trapped near a specific nanowaveguide (i.e. an optical nanofibre): (i) a conveyor belt-type tractor beam effect, (ii) an accelerator tractor beam effect, and (iii) a quantum coherent tractor beam effect, all of which can effectively pull atoms along the nanofibre toward the light source. This technique provides a new tool for controlling the motion of particles near nanowaveguides with potential applications in the study of particle transport and binding as well as atom interferometry.
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Affiliation(s)
- Mark Sadgrove
- Research Institute of Electrical Communications, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai-shi Japan
| | - Sandro Wimberger
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany
- Dipartimento di Fisica e Scienze della Terra, Universitádi Parma, Via G. P. Usberti 7/a, 43124 Parma, Italy
- INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Italy
| | - Síle Nic Chormaic
- Light-Matter Interactions Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
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8
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Carlo GG, Ermann L, Rivas AMF, Spina ME. Correspondence behavior of classical and quantum dissipative directed transport via thermal noise. Phys Rev E 2016; 93:042133. [PMID: 27176280 DOI: 10.1103/physreve.93.042133] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2016] [Indexed: 11/07/2022]
Abstract
We systematically study several classical-quantum correspondence properties of the dissipative modified kicked rotator, a paradigmatic ratchet model. We explore the behavior of the asymptotic currents for finite ℏ_{eff} values in a wide range of the parameter space. We find that the correspondence between the classical currents with thermal noise providing fluctuations of size ℏ_{eff} and the quantum ones without it is very good in general with the exception of specific regions. We systematically consider the spectra of the corresponding classical Perron-Frobenius operators and quantum superoperators. By means of an average distance between the classical and quantum sets of eigenvalues we find that the correspondence is unexpectedly quite uniform. This apparent contradiction is solved with the help of the Weyl-Wigner distributions of the equilibrium eigenvectors, which reveal the key role of quantum effects by showing surviving coherences in the asymptotic states.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Alejandro M F Rivas
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - María E Spina
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
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9
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Carlo GG, Rivas AMF, Spina ME. Classical to quantum correspondence in dissipative directed transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052907. [PMID: 26651762 DOI: 10.1103/physreve.92.052907] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Indexed: 06/05/2023]
Abstract
We compare the quantum and classical properties of the (quantum) isoperiodic stable structures [(Q)ISSs], which organize the parameter space of a paradigmatic dissipative ratchet model, i.e., the dissipative modified kicked rotator. We study the spectral behavior of the corresponding classical Perron-Frobenius operators with thermal noise and the quantum superoperators without it for small ℏ(eff) values. We find a remarkable similarity between the classical and quantum spectra. This finding significantly extends previous results-obtained for the mean currents and asymptotic distributions only-and, on the other hand, unveils a classical to quantum correspondence mechanism where the classical noise is qualitatively different from the quantum one. This is crucial not only for simple attractors but also for chaotic ones, where just analyzing the asymptotic distribution is revealed as insufficient. Moreover, we provide with a detailed characterization of relevant eigenvectors by means of the corresponding Weyl-Wigner distributions, in order to better identify similarities and differences. Finally, this model being generic, it allows us to conjecture that this classical to quantum correspondence mechanism is a universal feature of dissipative systems.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - Alejandro M F Rivas
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
| | - María E Spina
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina
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10
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11
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Wulf T, Petri C, Liebchen B, Schmelcher P. Symmetries and transport in site-dependent driven quantum lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042913. [PMID: 25375573 DOI: 10.1103/physreve.90.042913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2014] [Indexed: 06/04/2023]
Abstract
We explore the quantum dynamics of particles in a spatiotemporally driven lattice. A powerful numerical scheme is developed which provides us with the Floquet modes and thus enables a stroboscopic propagation of arbitrary initial states. A detailed symmetry analysis represents the cornerstone for an intricate manipulation of the Floquet spectrum. Specifically, we show how exact crossings can be converted into avoided ones, while the widths of these resulting avoided crossings can be engineered by adjusting parameters of the local driving. Asymptotic currents are shown to be controllable over a certain parameter range.
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Affiliation(s)
- Thomas Wulf
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Christoph Petri
- 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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12
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Carlo GG. Quantum isoperiodic stable structures and directed transport. PHYSICAL REVIEW LETTERS 2012; 108:210605. [PMID: 23003233 DOI: 10.1103/physrevlett.108.210605] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2012] [Indexed: 06/01/2023]
Abstract
It has been recently found that the so-called isoperiodic stable structures (ISSs) have a fundamental role in the classical current behavior of dissipative ratchets [Phys. Rev. Lett. 106, 234101 (2011).]. Here I analyze their quantum counterparts, the quantum ISSs (QISSs), which have a fundamental role in the quantum current behavior. QISSs have the simple attractor shape of those ISSs which settle down in short times. However, in the majority of the cases they are strongly different from the ISSs, looking approximately the same as the quantum chaotic attractors that are at their vicinity in parameter space. By adding thermal fluctuations of the size of ħ(eff) to the ISSs I am able to obtain very good approximations to the QISSs. I conjecture that in general, quantum chaotic attractors could be well approximated by means of just the classical information of a neighboring ISS plus thermal fluctuations. I expect to find this behavior in quantum dissipative systems in general.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, (C1429BNP) Buenos Aires, Argentina.
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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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Hagman H, Zelan M, Dion CM, Kastberg A. Directed transport with real-time steering and drifts along predesigned paths using a Brownian motor. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:020101. [PMID: 21405799 DOI: 10.1103/physreve.83.020101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2010] [Indexed: 05/30/2023]
Abstract
We have realized real-time steering of the directed transport in a Brownian motor based on cold atoms in optical lattices and demonstrate drifts along predesigned paths. The transport is induced by spatiotemporal asymmetries in the system, where we can control the spatial part, and we show that the response to changes in asymmetry is very fast. In addition to directional steering, a real-time control of the magnitude of the average drift velocity and an on-off switching of the motor are also demonstrated. We use a noninvasive real-time detection of the transport, enabling feedback control of the system.
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Affiliation(s)
- H Hagman
- Department of Physics, Umeå University, SE-901 87 Umeå, Sweden.
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Carlo GG, Ermann L, Borondo F, Benito RM. Environmental stability of quantum chaotic ratchets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:011103. [PMID: 21405657 DOI: 10.1103/physreve.83.011103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2010] [Indexed: 05/30/2023]
Abstract
The transitory and stationary behavior of a quantum chaotic ratchet consisting of a biharmonic potential under the effect of different drivings in contact with a thermal environment is studied. For weak forcing and finite ℏ, we identify a strong dependence of the current on the structure of the chaotic region. Moreover, we have determined the robustness of the current against thermal fluctuations in the very weak coupling regime. In the case of strong forcing, the current is determined by the shape of a chaotic attractor. In both cases the temperature quickly stabilizes the ratchet, but in the latter it also destroys the asymmetry responsible for the current generation. Finally, applications to isomerization reactions are discussed.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, C1429BNP Buenos Aires, Argentina
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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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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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Raviola LA, Carlo GG, Rivas AMF. Relatively robust classical structures in dissipative quantum chaotic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:047201. [PMID: 20481861 DOI: 10.1103/physreve.81.047201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2009] [Revised: 02/25/2010] [Indexed: 05/29/2023]
Abstract
We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the behavior of the purity, fidelity and Husimi distributions corresponding to initial states localized on short periodic orbits (scar functions) and map eigenstates. Scar functions, that have a fundamental role in the semiclassical description of chaotic systems, emerge as robust relative to other states (which are localized on classical structures) against environmental perturbations. Also, purity and fidelity show a complementary behavior as decoherence measures.
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Affiliation(s)
- Lisandro A Raviola
- Departamento de Física, CNEA, Avenida del Libertador 8250, C1429BNP Buenos Aires, Argentina
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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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Salger T, Kling S, Hecking T, Geckeler C, Morales-Molina L, Weitz M. Directed transport of atoms in a Hamiltonian quantum ratchet. Science 2009; 326:1241-3. [PMID: 19965469 DOI: 10.1126/science.1179546] [Citation(s) in RCA: 179] [Impact Index Per Article: 11.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Classical ratchet potentials, which alternate a driving potential with periodic random dissipative motion, can account for the operation of biological motors. We demonstrate the operation of a quantum ratchet, which differs from classical ratchets in that dissipative processes are absent within the observation time of the system (Hamiltonian regime). An atomic rubidium Bose-Einstein condensate is exposed to a sawtooth-like optical lattice potential, whose amplitude is periodically modulated in time. The ratchet transport arises from broken spatiotemporal symmetries of the driven potential, resulting in a desymmetrization of transporting eigenstates (Floquet states). The full quantum character of the ratchet transport was demonstrated by the measured atomic current oscillating around a nonzero stationary value at longer observation times, resonances occurring at positions determined by the photon recoil, and dependence of the transport current on the initial phase of the driving potential.
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Affiliation(s)
- Tobias Salger
- Institut für Angewandte Physik, Wegelerstrasse 8, 53115 Bonn, Germany.
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Bhattacharya S, Chaudhury P, Chattopadhyay S, Chaudhuri JR. Quantum transport in a periodic symmetric potential of a driven quantum system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041127. [PMID: 19905293 DOI: 10.1103/physreve.80.041127] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2009] [Indexed: 05/28/2023]
Abstract
A system-reservoir nonlinear coupling model has been proposed to the situation when the system is driven externally by a random force and the associated bath is kept in thermal equilibrium, in an attempt to put forth a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum Langevin equation in the overdamped limit (quantum Smoluchowski equation). We then obtain the analytical expression for phase induced quantum current in a periodic potential when the external noise has finite correlation time and explore the dependence of the current on various parameters related to the external noise, for example, the noise strength.
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Affiliation(s)
- Satyabrata Bhattacharya
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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23
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Zarlenga DG, Larrondo HA, Arizmendi CM, Family F. Complex synchronization structure of an overdamped ratchet with discontinuous periodic forcing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:011127. [PMID: 19658673 DOI: 10.1103/physreve.80.011127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/11/2009] [Indexed: 05/28/2023]
Abstract
A deterministic overdamped ratchet driven by a periodic square driving force is shown to display chaotic behavior. The system has neither temporal nor quenched noise but the strong nonlinearity of the driving force produces a very rich bifurcation pattern with synchronized as well as chaotic regions. This pattern disappears if a sinusoidal force replaces the square force. This unexpected behavior is explained by decomposing the system into two exactly solvable subsystems, each with its own characteristic transit time, so that the ratio between the period of the driving force and the transit times can be analyzed. The transition from synchronized to chaotic motion can be explained by means of a one-dimensional Poincaré map. Our results can be experimentally confirmed in a number of systems, including the three-junction superconducting quantum interference devices ratchet, the rocking ratchet effect for cold atoms, and the Josephson vortex ratchet.
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Affiliation(s)
- D G Zarlenga
- Departamento de Física, Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Avenida J.B. Justo 4302, 7600 Mar del Plata, Argentina
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24
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Ermann L, Carlo GG, Saraceno M. Behavior of the current in the asymmetric quantum multibaker map. Phys Rev E 2009; 79:056201. [PMID: 19518530 DOI: 10.1103/physreve.79.056201] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2008] [Revised: 02/24/2009] [Indexed: 11/07/2022]
Abstract
Recently, a new mechanism leading to purely quantum directed transport in the asymmetric multibaker map has been presented. Here, we show a comprehensive characterization of the finite asymptotic current behavior with respect to the h value, the shape of the initial conditions, and the features of the spectrum. We have considered different degrees of asymmetry in these studies and we have also analyzed the classical and quantum phase-space distributions for short times in order to understand the mechanisms behind the generation of the directed current.
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Affiliation(s)
- Leonardo Ermann
- Departamento de Física, CNEA, Libertador 8250, C1429BNP Buenos Aires, Argentina
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25
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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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26
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Carlo GG, Spina ME. Thermal effects on chaotic directed transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026212. [PMID: 19391825 DOI: 10.1103/physreve.79.026212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2008] [Indexed: 05/27/2023]
Abstract
We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite temperatures. We observe that the enhancement of the classical and quantum currents due to temperature depend strongly on the specific properties of the system. This makes it difficult to extract universal behaviors. We have also found that there is an analogy between the effects of the classical thermal noise and those of the finite h size. These results open many possibilities for their testing and implementation in kicked Bose-Einstein condensates and cold atoms experiments.
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Affiliation(s)
- Gabriel G Carlo
- Departamento de Física, CNEA, Libertador 8250, C1429BNP Buenos Aires, Argentina
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27
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Monteiro TS, Rançon A, Ruostekoski J. Nonlinear resonances in delta-kicked Bose-Einstein condensates. PHYSICAL REVIEW LETTERS 2009; 102:014102. [PMID: 19257197 DOI: 10.1103/physrevlett.102.014102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2008] [Indexed: 05/27/2023]
Abstract
We investigate the effect of atomic interactions on delta-kicked cold atoms. We show that the clearest signature of the nonlinear dynamics is a surprisingly abrupt cutoff that appears on the leading resonances. We show that this is due to an excitation path combining both Beliaev and Landau processes, with some analogies to nonlinear self-trapping. Investigation of dynamical instability reveals further symptoms of nonlinearity such as a regime of exponential oscillations.
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Affiliation(s)
- T S Monteiro
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
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28
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Poletti D, Alexander TJ, Ostrovskaya EA, Li B, Kivshar YS. Dynamics of matter-wave solitons in a ratchet potential. PHYSICAL REVIEW LETTERS 2008; 101:150403. [PMID: 18999576 DOI: 10.1103/physrevlett.101.150403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2008] [Indexed: 05/27/2023]
Abstract
We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.
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Affiliation(s)
- Dario Poletti
- Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542, Republic of Singapore
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29
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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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30
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Sadgrove M, Wimberger S, Parkins S, Leonhardt R. Scaling law and stability for a noisy quantum system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:025206. [PMID: 18850885 DOI: 10.1103/physreve.78.025206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2008] [Indexed: 05/26/2023]
Abstract
We show that a scaling law exists for the near-resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasiclassical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associated stability are confirmed by comparison with quantum simulations and experimental data.
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Affiliation(s)
- Mark Sadgrove
- CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
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31
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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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32
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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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33
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Wang J, Monteiro TS, Fishman S, Keating JP, Schubert R. Fractional variant Planck's over 2pi scaling for quantum kicked rotors without Cantori. PHYSICAL REVIEW LETTERS 2007; 99:234101. [PMID: 18233366 DOI: 10.1103/physrevlett.99.234101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2007] [Revised: 07/24/2007] [Indexed: 05/25/2023]
Abstract
Previous studies of quantum delta-kicked rotors have found momentum probability distributions with a typical width (localization length L) characterized by fractional variant Planck's over 2pi scaling; i.e., L approximately variant Planck's over 2pi;{2/3} in regimes and phase-space regions close to "golden-ratio" cantori. In contrast, in typical chaotic regimes, the scaling is integer, L approximately variant Planck's over 2pi;{-1}. Here we consider a generic variant of the kicked rotor, the random-pair-kicked particle, obtained by randomizing the phases every second kick; it has no Kol'mogorov-Arnol'd-Moser mixed-phase-space structures, such as golden-ratio cantori, at all. Our unexpected finding is that, over comparable phase-space regions, it also has fractional scaling, but L approximately variant Planck's over 2pi;{-2/3}. A semiclassical analysis indicates that the variant Planck's over 2pi;{2/3} scaling here is of quantum origin and is not a signature of classical cantori.
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Affiliation(s)
- J Wang
- Temasek Laboratories, National University of Singapore, 117542 Singapore
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34
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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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