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EPFL Press eBooks

Dynamics of Polariton Condensates in Double Wells

Konstantinos G. Lagoudakis

Published Dec 2, 2013• 0 citations
Publisher

Abstract

One of the most striking manifestations of the quantum collective behavior of matter is the Josephson effect: it allows for a classically forbidden current to flow without dissipation [125]. Traditional Josephson junctions are built by means of superconductors separated by thin non-conducting oxide barriers and they have drawn an intense interest for their striking phenomenology. A bosonic analog is the so-called Bosonic Josephson junction (BJJ) where two macroscopic populations of bosons are trapped in a double well geometry. Bose-Einstein condensation of dilute atomic gases has allowed for the demonstration of BJJs by trapping two condensates in double wells [126],[127].

DOI
10.1201/b15531-13

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One of the most striking manifestations of the quantum collective behavior of matter is the Josephson effect: it allows for a classically forbidden current to flow without dissipation [125]. Traditional Josephson junctions are built by means of superconductors separated by thin non-conducting oxide barriers and they have drawn an intense interest for their striking phenomenology. A bosonic analog is the so-called Bosonic Josephson junction (BJJ) where two macroscopic populations of bosons are trapped in a double well geometry. Bose-Einstein condensation of dilute atomic gases has allowed for the demonstration of BJJs by trapping two condensates in double wells [126],[127].
We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJ microscopic dynamics by means of extended Bose–Hubbard (EBH) models, which include usually neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJ macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility of distinguishing the Rabi, Josephson and Fock regimes in terms of the macroscopic parameters which appear in the EBH Hamiltonians, and then in the ODEs. We compare the predictions for the relative populations of the Bose gas atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross–Pitaevskii equations (GPEs). Our investigations show that the nonlinear terms of the ODEs are crucial to achieve a good agreement between the ODE and GPE approaches, and in particular to give quantitative predictions of the self-trapping regime.
Quantum phase transitions realized in inhomogeneous potentials is a topic of major importance in condensed matter physics. It involves non-trivial matter states, as Josephson oscillations for double potential wells [55], Mott insulators for periodic potentials [56], and Bose glasses for disorder potentials [57]. The case of disorder potentials is a crucial matter both for the intrinsic interest of phase transitions and for the unavoidable disorder in real systems. It is worth the effort to address this issue for the case of polariton condensates.
Bose Einstein condensates (BECs) in double well potentials have drawn a lot of attention for the possibilities they offer to study fundamental quantum mechanical effects at the macroscopic level as well as for potential applications like interferometry, high precision measurements or thermometry. In contrast to Josephson junctions realized in superconductors and superfluids, in BEC the interatomic interactions play a crucial role leading to anharmonic Josephson oscillations, if the initial population imbalance of the two wells is below a critical value, and to macroscopic quantum self-trapping i.e, inhibition of large amplitude Josephson oscillations above the threshold for the population imbalance. In this paper, a novel technique to adiabatically control of BEC in a double-well potential is proposed. The adiabatic dynamics of a BEC in a double well potential can be described in terms of a dark variable resulting from a combination of the population imbalance and the spatial atomic coherence.
We investigate the existence of the macroscopicmacroscopicmacroscopic quantumquantumquantum phasephasephase in trapped ultracold quantum degenerate gases, such as Bose-Einstein condensate, in an asymmetrical two-dimensional magnetic lattice. We show the key to adiabatically control the tunneling in the new two-dimensional magnetic lattice by means of external magnetic bias fields. The macroscopic quantum phase signature is identified as a Rabi-like oscillation when solving the system of coupled time-dependent differential equations, described here by the Boson Josephson Junctions (BJJs). In solving the system of the BJJs we used an order parameter that includes both time-dependent variational parameters which are the fractional population at each lattice site and the phase difference. The BJJs solution presents a clear evidence for the macroscopic quantum coherence.