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arXiv:1309.3488 · Physical Review A

Transport with ultracold atoms at constant density

Christian Nietner, Gernot Schaller, Tobias Brandes

Published Jan 6, 2014• 24 citations
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Abstract

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density-dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance, and thermopower. Considering ideal Fermi and Bose gas reservoirs, we observe steady-state currents against the thermal bias as a result of the nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.

DOI
10.1103/physreva.89.013605

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We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density-dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance, and thermopower. Considering ideal Fermi and Bose gas reservoirs, we observe steady-state currents against the thermal bias as a result of the nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.
We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.
We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix (SPDM) in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the SPDM in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer's conductance. It is shown that in the deep non-Markovian regime the transport current can be matched with that obtained by the non-equilibrium Green's function method.
We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source that models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock--Bogoliubov approximation. We apply this method to study the transport of dilute Bose gases through an atomic quantum dot and through waveguides with disorder. Our numerical simulations reveal that the onset of an explicitly time-dependent flow corresponds to the appearance of strong depletion of the condensate on the microscopic level and leads to a loss of global phase coherence.
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Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for 39K^{39}\mathrm{K}39K at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.
The transport properties of a bosonic chain have been calculated by placing the ends of the chain in contact with thermal and particle reservoirs at different temperatures and chemical potentials. The contact with the reservoirs is described by the use of a quantum Fokker-Planck-Kramers equation, which is a canonical quantization of the classical Fokker-Planck-Kramers equation. From the quantum equation we obtain equations for the covariances of the creation and annihilation boson operators and solve them in the stationary state for small interactions. From the covariances we determine the Onsager coefficients and in particular the conductance, which was found to be finite for any chain size leading to an infinite conductivity and the absence of Fourier's law.