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Register a new userQuantum resonances in an atom-optical delta-kicked harmonic oscillator
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Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum resonances that could be observed in such a system. Having outlined our model of the physical system we derive the values at which quantum resonances occur and relate these to potential experimental parameters. We discuss the observable effects of the quantum resonances, using the results of numerical simulations. We develop a physical explanation for the quantum resonances based on symmetries shared between the classical phase space and the quantum-mechanical time evolution operator. We explore the evolution of coherent states in the system by reformulating the dynamics in terms of a mapping over an infinite, two-dimensional set of coefficients, from which we derive an analytic expression for the evolution of a coherent state at quantum resonance.
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We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos on the one hand, and ballistic or diffusive energy absorption on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high resolution Wigner functions at long times, where the system approaches a quasi-stationary cyclic evolution. Thereby, we are able to perform an accurate study of the thermodynamic properties of a non-integrable, quantum chaotic system in contact with a heat bath.
The study of quantum resonances in the chaotic atom-optics kicked rotor system is of interest from two different perspectives. In quantum chaos, it marks out the regime of resonant quantum dynamics in which the atomic cloud displays ballistic mean energy growth due to coherent momentum transfer. Secondly, the sharp quantum resonance peaks are useful in the context of measurement of Talbot time, one of the parameter that helps in precise measurement of fine structure constant. Most of the earlier works rely on fidelity based approach and have proposed Talbot time measurement through experimental determination of the momentum space probability density of the periodically kicked atomic cloud. Fidelity approach has the disadvantage that phase reversed kicks need to be imparted as well which potentially leads to dephasing. In contrast to this, in this work, it is theoretically shown that, without manipulating the kick sequences, the quantum resonances through position space density can be measured more accurately and is experimentally feasible as well.
We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We exactly compute the characteristic function of the heat distribution and show that it verifies the Jarzynski-Wojcik fluctuation theorem. We further evaluate the heat probability density in the limit of long thermalization times, both in the low and high temperature regimes, and investigate its time evolution by calculating its first two cumulants.
We propose a novel platform for the investigation of quantum wave packet dynamics, offering a complementary approach to existing theoretical models and experimental systems. It relies on laser-cooled neutral atoms which orbit around an optical nanofiber in an optical potential produced by a red-detuned guided light field. We show that the atomic center-of-mass motion exhibits genuine quantum effects like collapse and revival of the atomic wave packet. As distinctive advantages, our approach features a tunable dispersion relation as well as straightforward readout for the wave packet dynamics and can be implemented using existing quantum optics techniques.
Bose-Einstein condensates subject to short pulses (`kicks) from standing waves of light represent a nonlinear analogue of the well-known chaos paradigm, the quantum kicked rotor. Previous studies of the onset of dynamical instability (ie exponential proliferation of non-condensate particles) suggested that the transition to instability might be associated with a transition to chaos. Here we conclude instead that instability is due to resonant driving of Bogoliubov modes. We investigate the excitation of Bogoliubov modes for both the quantum kicked rotor (QKR) and a variant, the double kicked rotor (QKR-2). We present an analytical model, valid in the limit of weak impulses which correctly gives the scaling properties of the resonances and yields good agreement with mean-field numerics.
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