arXiv subjects

S. A. Gardiner

Publications and source records attributed to S. A. Gardiner.

At least 37 records · Page 2Linked to original sources

arXiv2011

Coherence and Instability in a Driven Bose-Einstein Condensate: A Fully Dynamical Number-Conserving Approach

We consider a Bose-Einstein condensate driven by periodic delta-kicks. In contrast to first-order descriptions, which predict rapid, unbounded growth of the noncondensate in resonant parameter regimes, the consistent treatment of condensate depletion in our fully-time-dependent, second-order description acts to damp this growth, leading to oscillations in the (non)condensate population and the coherence of the system.

cond-mat.quant-gas↗

arXiv2010

Realizing bright matter-wave soliton collisions with controlled relative phase

We propose a method to split the ground state of an attractively interacting atomic Bose-Einstein condensate into two bright solitary waves with controlled relative phase and velocity. We analyze the stability of these waves against their subsequent re-collisions at the center of a cylindrically symmetric, prolate harmonic trap as a function of relative phase, velocity, and trap anisotropy. We show that the collisional stability is strongly dependent on relative phase at low velocity, and we identify previously unobserved oscillations in the collisional stability as a function of the trap anisotropy. An experimental implementation of our method would determine the validity of the mean field description of bright solitary waves, and could prove an important step towards atom interferometry experiments involving bright solitary waves.

cond-mat.quant-gas↗

arXiv2010

Rotational Response of Two-Component Bose-Einstein Condensates in Ring Traps

We consider a two-component Bose-Einstein condensate (BEC) 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 either through 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.

cond-mat.quant-gas↗

arXiv2009

Conical intersections in laboratory coordinates with ultracold molecules

For two states of opposite parity that cross as a function of an external magnetic field, the addition of an electric field will break the symmetry and induce an avoided crossing. A suitable arrangement of fields may be used to create a conical intersection as a function of external spatial coordinates. We consider the effect of the resulting geometric phase for ultracold polar molecules. For a Bose-Einstein condensate in the mean-field approximation, the geometric phase effect induces stable states of persistent superfluid flow that are characterized by half-integer quantized angular momentum.

cond-mat.quant-gas↗

arXiv2009

Quantum resonances in an atom-optical delta-kicked harmonic oscillator

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.

quant-ph↗

arXiv2008

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 one. 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.

physics.atom-ph↗

arXiv2008

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 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.

physics.atom-ph↗

arXiv2007

Bright Solitary-Matter-Wave Collisions in a Harmonic Trap: Regimes of Soliton-like Behaviour

Systems of solitary-waves in the 1D Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyse the soliton-like nature of these solitary-waves, a particle analogy for the solitary-waves is formulated. Exact soliton solutions exist in the absence of an external trapping potential, which behave in a particle-like manner, and we find the particle analogy we employ to be a good model also when a harmonic trapping potential is present. In the case of two solitons, the particle model is integrable, and the dynamics are completely regular. The extension to three particles supports chaotic regimes. The agreement between the particle model and the wave dynamics remains good even in chaotic regimes. In the case of a system of two solitary waves of equal norm, the solitons are shown to retain their phase difference for repeated collisions. This implies that soliton-like regimes may be found in 3D geometries where solitary waves can be made to repeatedly collide out of phase, stabilising the condensate against collapse.

cond-mat.other↗

arXiv2007

The 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 non-interacting 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 centre of mass momentum eigenstates with varying quasimomentum, and we have determined analytic expressions for the evolution of the second-order momentum moment to illustrate the range of behaviours.

physics.atom-ph↗

arXiv2007

A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas

We describe a number conserving approach to the dynamics of Bose-Einstein condensed dliute atomic gases. This builds upon the works of Gardiner [C. W. Gardiner, Phys. Rev. A 56, 1414 (1997)], and Castin and Dum [Y. Castin and R. Dum, Phys. Rev. A 57, 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of non-condensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a second-order treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and non-condensate number dynamics for a finite total number of particles, and show that such a second-order treatment is provided by a suitably generalized Gross-Pitaevskii equation, coupled to the Castin-Dum number-conserving formulation of the Bogoliubov-de Gennes equations. The necessary equations of motion can be generated from an approximate third-order Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics occurring at finite temperature, where there is a significant non-condensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant non-condensate fraction, even if the non-condensate fraction is initially negligible.

cond-mat.other↗

arXiv2006

Bright Matter-Wave Soliton Collisions in a Harmonic Trap: Regular and Chaotic Dynamics

Collisions between bright solitary waves in the 1D Gross-Pitaevskii equation with a harmonic potential, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. A particle analogy for the solitary waves is formulated, which is shown to be integrable for a two-particle system. The extension to three particles is shown to support chaotic regimes. Good agreement is found between the particle model and simulations of the full wave dynamics, suggesting that the dynamics can be described in terms of solitons both in regular and chaotic regimes, thus presenting a paradigm for chaos in wave-mechanics.

cond-mat.other↗

arXiv2006

Quantum Accelerator Modes from the Farey Tree

We show that mode-locking finds a purely quantum non-dissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode-locking. A hierarchy for the rational numbers known as the Farey Tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.

physics.atom-ph↗

arXiv2005

Quantum random walks using quantum accelerator modes

We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create co-existent quantum accelerator modes, and hence how momentum transfer that depends on the atoms' internal state can be achieved. When combined with microwave driving of the transition between the states, a new type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes.

physics.atom-ph↗

arXiv2004

Quantum Mechanical Cumulant Dynamics near Stable Periodic Orbits in Phase Space: Application to the classical-like dynamics of quantum accelerator modes

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wavepackets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wavefunction dynamics.

physics.atom-ph↗

arXiv2004

Gravity-Sensitive Quantum Dynamics in Cold Atoms

We subject a falling cloud of cold cesium atoms to periodic kicks from a sinusoidal potential created by a vertical standing wave of off-resonant laser light. By controllably accelerating the potential, we show quantum accelerator mode dynamics to be highly sensitive to the effective gravitational acceleration when this is close to specific, resonant values. This quantum sensitivity to a control parameter is reminiscent of that associated with classical chaos, and promises techniques for precision measurement.

physics.atom-ph↗

arXiv2002

Signatures of quantum stability in a classically chaotic system

We experimentally and numerically investigate the quantum accelerator mode dynamics of an atom optical realization of the quantum delta-kicked accelerator, whose classical dynamics are chaotic. Using a Ramsey-type experiment, we observe interference, demonstrating that quantum accelerator modes are formed coherently. We construct a link between the behavior of the evolution's fidelity and the phase space structure of a recently proposed pseudoclassical map, and thus account for the observed interference visibilities.

physics.atom-ph↗

arXiv2002

Experimental observation of high-order quantum accelerator modes

Using a system consisting of a freely falling cloud of cold cesium atoms periodically kicked by pulses from a vertical standing wave of laser light, we present the first experimental observation of high-order quantum accelerator modes. This confirms the recent prediction by Fishman, Guarneri, and Rebuzzini [Phys. Rev. Lett. 89, 084101 (2002)]. We also show how these accelerator modes can be identified with the stable regions of phase space in a classical-like chaotic system, despite their intrinsically quantum origin.

physics.atom-ph↗

arXiv2002

(Quantum) Chaos in BECs

I consider general connections between chaotic and quantum chaotics dynamics in single particles, and the effect of adding comparable ``chaos-inducing'' potentials to a Bose-condensed system, considering in particular concepts of integrability and the effect of particle loss from the condensate mode.

cond-mat.soft↗