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arXiv:cond-mat/9902110 · Journal of Optics B Quantum and Semiclassical Optics

Dressed states of a two component Bose-Einstein condensate

P. B. Blakie, R. J. Ballagh, Crispin W. Gardiner

Published Aug 1, 1999• 21 citations
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Abstract

A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross-Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates numerically in the case of one spatial dimension, and explore their properties as a function of system parameters. In contrast to the quantum optical case, the condensate dressed states exhibit spatial behaviour which depends on the system parameters, and can be manipulated by changing the cw external field.

DOI
10.1088/1464-4266/1/4/304

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A condensate with two internal states coupled by external electromagnetic radiation, is described by coupled Gross-Pitaevskii equations, whose eigenstates are analogous to the dressed states of quantum optics. We solve for these eigenstates numerically in the case of one spatial dimension, and explore their properties as a function of system parameters. In contrast to the quantum optical case, the condensate dressed states exhibit spatial behaviour which depends on the system parameters, and can be manipulated by changing the cw external field.
We consider a two-component weakly interacting Bose-Einstein condensate in the presence of an external field which couples the two components. We express the Hamiltonian in terms of the energy eigenstates of the single-body part of the Hamiltonian. These eigenstates are the atomic dressed states of quantum optics. When the energy difference between the two dressed states is much larger than the mean-field interactions, two-body interactions in the dressed state basis that do not conserve the number of atoms in each of the two dressed states are highly suppressed. The two-body interactions then take on a simplified form in the dressed basis with effective coupling constants that depend on the intensity and frequency of the external field. This implies that the chemical potential as well as the quasiparticle spectrum may be controlled experimentally in a simple manner. We demonstrate this by showing that one may achieve significant variations in the speed of sound in the condensate, a quantity which has been measured experimentally.
Dressed potentials realized by coupling state-dependent bare potentials with external fields have important applications in trapping and manipulating atoms. Here, we study the dynamics of dressed states for coupled two-component Bose-Einstein condensates (BECs) in state-dependent potentials. Through both analytical and numerical methods, we find that the dressed state dynamics sensitively depend on both the inter-component coupling strength and the initial state. If the inter-component coupling is strong enough and the initial wave packet is located at the potential minimum, the dressed states can be decoupled and the Josephson oscillations and macroscopic quantum self-trapping appear. However, if the initial wave packet is located far away from the potential minimum, the wave packet will acquire a large kinetic energy and Landau-Zener transitiozs between the dressed states occur at the avoided-crossing point. Further, we give the validity ranges and conditions for the formation of adiabatic potentials, where the influences of Landau-Zener transitions can be ignored. Our results give an insight on how the inter-component coupling affects the dressed state dynamics and how to realize adiabatic potentials with BECs in state-dependent potentials.
We study the dynamics of weakly interacting Bose-Einstein condensates consisting of alkali atoms with two or more internal eigenstates. Three separate problems are examined in this thesis, which look at the behavior of the condensates in the presence of electromagnetic fields, which couple the internal states of the atoms. First, we examine the ground state and quasiparticle excitations for a condensate with a spatially uniform and time independent field, which couples two of the internal states. In particular, we address the nature of the instabilities that have been predicted in these systems. Second, we look at the time evolution of small condensates with a time dependent field, which couples two states. It is shown that the atomic population in the two components, as a function of time, is very different for a condensate with a precisely defined number of atoms and one that exhibits spontaneous symmetry breaking. Finally, we propose two methods for mapping information about the quantum state of the condensate to a mode of an electromagnetic cavity. The first method, which is irreversible, is only able to transfer the population statistics of the condensate to the cavity field. The second method involves the adiabatic transfer of the quantum state of the condensate to the cavity field.
The achievement of Bose-Einstein condensation (BEC) in ultracold vapors of alkali atoms has given enormous impulse to the theoretical and experimental study of dilute atomic gases in condensed quantum states inside magnetic traps and optical lattices. This article offers a short survey on mathematical models and theories as well as numerical methods for BEC based on the mean field theory. We start with the Gross-Pitaevskii equation (GPE) in three dimensions (3D) for modeling one-component BEC of the weakly interacting bosons, scale it to obtain a three-parameter model and show how to reduce it to two dimensions (2D) and one dimension (1D) GPEs in certain limiting regimes. Mathematical theories and numerical methods for ground states and dynamics of BEC are provided. Extensions to GPE with an angular momentum rotation term for a rotating BEC, to GPE with long-range anisotropic dipole-dipole interaction for a dipolar BEC and to coupled GPEs for spin-orbit coupled BECs are discussed. Finally, some conclusions are drawn and future research perspectives are discussed.
The properties of traps for exciton polaritons in a semiconductor optical microcavity with an embedded quantum well were considered. The two-component Bose condensate of photons and excitons was described by a coupled system of equations similar to the Gross-Pitaevskii equations, and analytical solutions in the Thomas-Fermi approximation were obtained for traps with weak exciton confinement. For strong confinement, condensate behavior was investigated numerically, and spatial profiles of coupled condensates of excitons and photons (which appear to be different in general case) were determined.
We study the dynamics of a two-component Bose-Einstein condensate where the two components are coupled via an optical lattice. In particular, we focus on the dynamics as one drives the system through a critical point of a first-order phase transition characterized by a jump in the internal populations. Solving the time-dependent Gross-Pitaevskii equation, we analyze the breakdown of adiabaticity, impact of nonlinear atom-atom scattering, and role of a harmonic trapping potential. Our findings demonstrate that the phase transition is resilient to both contact interaction between atoms and external trapping confinement.