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arXiv:1512.07946 · New Journal of Physics

Complete population inversion of Bose particles by an adiabatic cycle

Atushi Tanaka, Taksu Cheon

Published Apr 27, 2016• 3 citations
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Abstract

We show that an adiabatic cycle excites Bose particles confined in a one-dimensional box. During the adiabatic cycle, a wall described by a δ -shaped potential is applied and its strength and position are slowly varied. When the system is initially prepared in the ground state, namely, in the zero-temperature equilibrium state, the adiabatic cycle brings all Bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of Bosons.

DOI
10.1088/1367-2630/18/4/045023

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We show that an adiabatic cycle excites Bose particles confined in a one-dimensional box. During the adiabatic cycle, a wall described by a δ -shaped potential is applied and its strength and position are slowly varied. When the system is initially prepared in the ground state, namely, in the zero-temperature equilibrium state, the adiabatic cycle brings all Bosons into the first excited one-particle state, leaving the system in a nonequilibrium state. The absorbed energy during the cycle is proportional to the number of Bosons.
An adiabatic cycle involving the δ-function potential is shown to excite Bose particles confined in a one-dimensional box.We consider a cycle, during which a wall described by a δ potential is applied and its strength and position are slowly varied.When the system is initially prepared in the equilibrium ground state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a nonequilibrium state.The absorbed energy during the cycle is proportional to the number of bosons.
It is shown, through a mean-field description, that the ground state of weakly interacting Bose particles in a quasi-one-dimensional box trap can be converted into an excited stationary state by an almost adiabatic cyclic operation that involves a quench: A sharp impurity potential is applied, and its strength is varied during the cycle, which induces a nonequilibrium stationary state exhibiting the inversion of population. This process is robust in the sense that the resultant stationary state is almost independent of the details of the cycle, such as the position of the impurity, as long as the cycle is far enough from critical regions. The case of the failure of the population inversion due to the strong interparticle interactions is also examined.
Adiabatic excitation of a confined one-dimensional particle with a variable δ\deltaδ-wall
It is shown that adiabatic cycles excite a quantum particle, which is confined in a one-dimensional region and is initially in an eigenstate. During the cycle, a δ\deltaδ-wall is applied and varied its strength and position. After the completion of the cycle, the state of the particle arrives another eigenstate. It is also shown that an arbitrary pair of eigenstates can be connected through a combination of adiabatic cycles. A detailed argument is provided for the case that the particle is confined by an infinite square well. This is an example of exotic quantum holonomy in Hamiltonian systems.
It is shown that adiabatic cycles excite a quantum particle, which is confined in a one-dimensional region and is initially in an eigenstate. During the cycle, an infinitely sharp wall is applied and its strength and position are varied. After the completion of the cycle, the state of the particle arrives at another eigenstate. It is also shown that we may vary the final adiabatic state by choosing the parameters of the cycle. With a combination of these adiabatic cycles, we can connect an arbitrary pair of eigenstates. Hence, these cycles may be regarded as the basis of the adiabatic excitations. A detailed argument is provided for the case that the particle is confined by an infinite square well. This is an example of exotic quantum holonomy in Hamiltonian systems.
In Bose-Einstein condensation, a macroscopically large number of particles occupy the same single-particle quantum state. Our goal is to study time-dependent aspects of particle excitations to states other than the single-particle macroscopic state in trapped dilute atomic gases. We adopt the view that atoms are excited in pairs so that their scattering from the single-particle state to vector positions x and y at time t is described by the pair-excitation function, K0(x,y,t). We solve a nonlocal equation for K0 under a slowly varying external potential by assuming that the wave function of the macroscopic state satisfies a time-independent nonlinear Schroedinger equation. For zero initial excitation (K0=0 at t=0) and sufficiently large t, we evaluate asymptotically K0 in terms of the one-variable Lommel function for any distance |x-y|.
The properties of a one-dimensional system of bosons interacting via a repulsive delta-function potential are studied here using a modified Bogolyubov method. The motivation for the modification is twofold: First, to cure an internal inconsistency that predicts a single-particle ground-state occupancy of minus infinity when the Bogolyubov scheme is applied to this model. Second, to abandon the initial assumption---at odds with the exact result---of a macroscopically occupied single-particle ground-state. Whereas the Bogolyubov scheme uses the lowest-energy-single-particle state as a reservoir for the other states, our method uses, for each single-particle state, all single-particle states of lower energy collectively as a reservoir. This not only removes the inconsistency but also allows us to estimate the ground-state energy in much better agreement with the exact result.