Rotational response of two-component Bose-Einstein condensates in ring traps

We consider a two-component Bose-Einstein condensate in a ring trap in a rotating frame and show how to determine the response of such a configuration to being in a rotating frame via accumulation of a Sagnac phase. This may be accomplished through either population oscillations or the motion of spatial-density fringes. We explicitly include the effect of interactions via a mean-field description and study the fidelity of the dynamics relative to an ideal configuration

Manifestation of quantum resonances and antiresonances in a finite temperature dilute atomic gas

We investigate the effect of temperature on resonant and antiresonant dynamics in a dilute atomic gas kicked periodically by a standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and show that the atomic dynamics are highly sensitive to the initial momentum width of the gas. We explain this sensitivity by examining the time evolution of individual atomic center-of-mass momentum eigenstates with varying quasimomentum, and we determine analytic expressions for the evolution of the second-order momentum moment to illustrate the range of behaviors

Driving the resonant quantum kicked rotor via extended initial conditions

We study the resonances of the quantum kicked rotor subjected to an extended initial distribution. For the primary resonances we obtain the dispersion relation for the map of this system. We find an analytical dependence of the statistical moments on the shape of the initial distribution. For the secondary resonances we obtain numerically a similar dependence. This allows us to devise an extended initial condition which produces an average angular momentum pointing in a preset direction which increases with time with a preset ratio.Comment: 6 pages, 5 figures, send to EPJ

Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator

We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular, we consider the dynamical evolution of the momentum moments and find that all even-ordered momentum moments exhibit a power-law growth. In the ultracold (zero-temperature) limit the exponent is determined by the order of the moment, whereas for a broad, thermal initial momentum distribution the exponent is reduced by 1. To demonstrate the power-law behavior explicitly we consider the evolutions of the second- and fourth-order momentum moments, and cumulants, for an initially Gaussian momentum distribution corresponding to the Maxwell-Boltzmann distribution of an ideal gas at thermal equilibrium

Fractional resonances in the atom-optical delta-kicked accelerator

We consider resonant dynamics in a dilute atomic gas falling under gravity through a periodically pulsed standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and we show that quantum resonances are highly sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. For particular values of the atomic acceleration, we observe fractional resonances. We investigate the effect of the initial atomic momentum width on the fractional resonances and quantify the sensitivity of fractional resonances to thermal effects

Quantum resonant effects in the delta-kicked rotor revisited

We review the theoretical model and experimental realization of the atom optics $\delta-$kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy $/2m$ in units of the recoil energy $E_{rec} = \hbar \omega_{rec}$. The energy of the system is examined as a function of pulse period for a range of kicks that allow the observation of quantum resonances. In particular we study the behavior of these resonances for a large number of kicks. Higher order quantum resonant effects corresponding to the fractional Talbot time of (1/4)$T_{T}$ and (1/5)$T_{T}$ for five and ten kicks have been observed. Moreover, we describe the effect of the initial momentum of the atoms on quantum resonances in the AOKR.Comment: 30 pages, 17 figure