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arXiv:cond-mat/0012010 · Physical Review A

Manipulating the speed of sound in a two-component Bose-Einstein condensate

Christopher P. Search, P. R. Berman

Published Mar 20, 2001• 20 citations
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Abstract

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.

DOI
10.1103/physreva.63.043612

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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.
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 dilute homogenous atomic Bose-Einstein condensate with two nondegenerate internal energy levels that achieve a state of chemical equilibrium in the presence of an external radiation field that couples the two states. The presence of the radiation field can result in new ground states for the condensate as a consequence of the lowering of the condensate energy due to the interaction energy with the field. We analyze the ground-state energy as a function of the coupling constants for the two-body interactions, the Rabi frequency of the radiation field, and the detuning of the field, and we give explicit expressions for the quasiparticle excitation spectrum.
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.
In this thesis a number of aspects on possible manipulation of Bose-Einstein condensate in trapped atomic gases is investigated. First, a model for atom optical experiments involving Bose condensates is proposed and numerical simulations are presented to illustrate its characteristics. We demonstrate ways of focusing and splitting the condensate by modifying experimentally adjustable parameters. We show that there are at least two ways of implementing atom optical elements: one may modulate the interatomic scattering length in space, or alternatively, use a sinusoidal, externally applied potential. The temporal evolution of quasiparticle excitations is studied via the Gross-Pitaevskii Equation. Nonlinear mode mixing of quasiparticles is introduced, and is observed using a quasiparticle projection method. This is used as a basis of time-dependent finite temperature simulations, which we argue to be valid under regimes of high occupation number. An illustration via a closely related evaporative cooling simulation is provided. A phenomenological damping formalism for superfluidity near the λ point is adopted to describe the damping of excitations in a Bose-Einstein condensate. An estimate for the damping parameter is found. The damping formalism as a numerical tool to calculate the ground eigenstate of the condensate is explored. A novel, experimentally realisable interferometry for Bose-Einstein condensates using near-field diffraction is proposed. The scheme is based on the phenomenon of intermode traces or quantum carpets; we demonstrate the structured spatio-temporal pattern for the dilute, atomic Bose-Einstein condensate. The pattern is found to change with temperature, which allows us to perform interferometric temperature measurements. Finally, an output coupler for Bose-Einstein Condensates based on stimulated Raman transition is investigated. The spectrum and coherence are calculated for an atomic beam slowly coupled out of a trap containing a partially condensed Bose gas at finite temperatures. A number conserving Hartree-Fock-Bogliubov formalism has been used to incorporate finite temperature effects. Various different processes are found to become dominant for a suitable choice of the coupling parameters.
For the case of an atomic Bose-Einstein condensate formed in a symmetrical double-well potential with well-separated minima, the dynamics of Bose-condensed atoms interacting with a single-mode quantized traveling-wave laser field are investigated in detail. By considering the system consisting of the Bose-condensed atoms and laser field with and without dissipation, the eigenstates and eigenvalues of the corresponding Hamiltonian for both cases are obtained. The time development of the Bose-condensed state plays a major role in the discussion. It is shown that the probability of finding all atoms in the Bose-condensed state displays an undamped oscillatory behavior in the absence of dissipation and a damped oscillatory behavior in the presence of dissipation. Moreover, it is found that the tunneling effect can increase the oscillatory frequency among the dressed bosonic states and affect the dynamics of the system. As an application of these results, a characteristic time that may be used to evaluate the number of condensed atoms is introduced.
Using the time-dependent Bogoliubov approach, we study adiabaticity for a two-component Bose-Einstein condensate in a three-dimensional time-dependent optical lattice with unit filling, in the superfluid and weakly interacting regime. We show that raising the lattice potential height can couple the ground state of the Bogoliubov Hamiltonian to excited states with two quasiparticles of opposite quasimomenta. In the symmetric case for interactions and density in the two components these represent sound waves where the two components oscillate out of phase. We find an analytic expression for the adiabatic time, its dependence on the fraction of atoms in each component, and its scaling with the system size.