Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0803.1229 · Physical Review A

Atomic current in optical lattices: Reexamination of the Esaki-Tsu equation

Andrey R. Kolovsky

Published Jun 5, 2008• 14 citations
arXivHTMLPDF

Abstract

This paper discusses the master equation approach to the derivation of the Esaki-Tsu equation for drift current. It is shown that the relaxation term in the master equation can be identified by measuring the velocity distribution of the carriers. We also show that the standard form of the relaxation term, used earlier to derive the Esaki-Tsu equation, predicts unphysical velocity distribution. We suggest a more elaborate relaxation term, which is argued to correctly capture the effect of a bosonic bath in experiments on atomic current in optical lattices.

DOI
10.1103/physreva.77.063604

Related papers

Observation of Landau-Zener tunneling through atomic current in the optical lattices

Jie-Yun Yan, Suqing Duan, Wei Zhang +1 more

The atomic current in the Fourier-synthesized optical lattices under a constant external force is investigated theoretically. Based on a two-band model, the atomic current is derived by solving the Boltzmann equations. We find that the stationary atomic current changes with the probability of Landau-Zener tunneling, depending on the adjustable energy structure of the optical lattices. In contrast to the classical results of an electron in superlattices given by the Esaki-Tsu equations, the relation between the stationary atomic current and the strength of the external force in optical lattices is modified significantly. Both these characteristics can be taken as an effective way to observe the Landau-Zener tunneling in the optical lattices.

Physical Review A•May 8, 2009•5 citations

Conductivity with cold atoms in optical lattices

Andrey R. Kolovsky

This paper studies a simple model of conductivity—a quantum particle (an atom) in a lattice, subject to a static field and interacting with the bath of Bose atoms. Results from direct numerical simulations of the system dynamics and statistical analysis of the eigenstates are compared with predictions from linear response theory, analytical solutions of the master equation, and the theory of quantum chaos. It is shown, in particular, that the behavior of the current–current correlation function, entering Kubo’s equation, is entirely defined by the chaotic properties of the system and that the phenomenological relaxation constant, entering the master equation, is actually encoded in this correlation function.

Journal of Statistical Mechanics Theory and Experiment•Feb 4, 2009•6 citations

Background atoms and decoherence in optical lattices

Krzysztof Pawłowski, Kazimierz Rza̧żewski

All experiments with ultracold atoms are performed in the presence of background residual gas. With the help of a suitable master equation we investigate a role of these fast atoms on the loss of coherence in optical lattices. We present an exact solution of the master equation and give the analytic formulas for all correlation functions in the presence of one-body losses. Additionally we discuss the existence of a Schr\"odinger cat state predicted in this system in Greiner et al. [Nature 419, 51 (2002)].

arXiv:0909.2515•Physical Review A•Jan 20, 2010•18 citations

Transport of strong-coupling polarons in optical lattices

M Bruderer, A Klein, S R Clark +1 more

We study the transport of ultracold impurity atoms immersed in a Bose–Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model, we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki–Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.

arXiv:0710.4493•New Journal of Physics•Mar 11, 2008•63 citations

Open quantum systems approach to atomtronics

Ronald Pepino, J. Cooper, D. Meiser +2 more

We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate and logic gate behavior in an optical lattice.

arXiv:1005.3069•Physical Review A•Jul 28, 2010•52 citations

Field-theoretical derivation of the master equation in quantum optics

Hans C. Fogedby

The basic tool in quantum optics for the description of atomic systems interacting with coherent and incoherent radiation fields is the atomic density matrix governed by the master equation. In the present paper we apply standard condensed-matter nonequilibrium many-body methods to the problem of a two-level atom driven by an external laser field and relaxing by interaction with the radiation field. We recover the well-known dressed-atom picture and, in particular, we present an alternative derivation of the master equation for the atomic density matrix which allows simple generalizations.

Physical Review A•May 1, 1993•4 citations
This paper discusses the master equation approach to the derivation of the Esaki-Tsu equation for drift current. It is shown that the relaxation term in the master equation can be identified by measuring the velocity distribution of the carriers. We also show that the standard form of the relaxation term, used earlier to derive the Esaki-Tsu equation, predicts unphysical velocity distribution. We suggest a more elaborate relaxation term, which is argued to correctly capture the effect of a bosonic bath in experiments on atomic current in optical lattices.
The atomic current in the Fourier-synthesized optical lattices under a constant external force is investigated theoretically. Based on a two-band model, the atomic current is derived by solving the Boltzmann equations. We find that the stationary atomic current changes with the probability of Landau-Zener tunneling, depending on the adjustable energy structure of the optical lattices. In contrast to the classical results of an electron in superlattices given by the Esaki-Tsu equations, the relation between the stationary atomic current and the strength of the external force in optical lattices is modified significantly. Both these characteristics can be taken as an effective way to observe the Landau-Zener tunneling in the optical lattices.
This paper studies a simple model of conductivity—a quantum particle (an atom) in a lattice, subject to a static field and interacting with the bath of Bose atoms. Results from direct numerical simulations of the system dynamics and statistical analysis of the eigenstates are compared with predictions from linear response theory, analytical solutions of the master equation, and the theory of quantum chaos. It is shown, in particular, that the behavior of the current–current correlation function, entering Kubo’s equation, is entirely defined by the chaotic properties of the system and that the phenomenological relaxation constant, entering the master equation, is actually encoded in this correlation function.
All experiments with ultracold atoms are performed in the presence of background residual gas. With the help of a suitable master equation we investigate a role of these fast atoms on the loss of coherence in optical lattices. We present an exact solution of the master equation and give the analytic formulas for all correlation functions in the presence of one-body losses. Additionally we discuss the existence of a Schr\"odinger cat state predicted in this system in Greiner et al. [Nature 419, 51 (2002)].
We study the transport of ultracold impurity atoms immersed in a Bose–Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model, we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki–Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.
We derive a quantum master equation to treat quantum systems interacting with multiple reservoirs. The formalism is used to investigate the atomic transport of bosons across a variety of lattice configurations. We demonstrate how the behavior of an electronic diode, a field-effect transistor, and a bipolar junction transistor can be realized with neutral, ultracold atoms trapped in optical lattices. An analysis of the current fluctuations is provided for the case of the atomtronic diode. Finally, we show that it is possible to demonstrate and logic gate behavior in an optical lattice.
The basic tool in quantum optics for the description of atomic systems interacting with coherent and incoherent radiation fields is the atomic density matrix governed by the master equation. In the present paper we apply standard condensed-matter nonequilibrium many-body methods to the problem of a two-level atom driven by an external laser field and relaxing by interaction with the radiation field. We recover the well-known dressed-atom picture and, in particular, we present an alternative derivation of the master equation for the atomic density matrix which allows simple generalizations.