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C. W. Gardiner

Publications and source records attributed to C. W. Gardiner.

At least 37 records · Page 2Linked to original sources
arXiv2004

A phase-space method for the Bose-Hubbard model

We present a phase-space method for the Bose-Hubbard model based on the Q-function representation. In particular, we consider two model Hamiltonians in the mean-field approximation; the first is the standard "one site" model where quantum tunneling is approximated entirely using mean-field terms; the second "two site" model explicitly includes tunneling between two adjacent sites while treating tunneling with other neighbouring sites using the mean-field approximation. The ground state is determined by minimizing the classical energy functional subject to quantum mechanical constraints, which take the form of uncertainty relations. For each model Hamiltonian we compare the ground state results from the Q-function method with the exact numerical solution. The results from the Q-function method, which are easy to compute, give a good qualitative description of the main features of the Bose-Hubbard model including the superfluid to Mott insulator. We find the quantum mechanical constraints dominate the problem and show there are some limitations of the method particularly in the weak lattice regime.

cond-mat.soft↗
arXiv2003

Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields

A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which takes account of anticommutation relations between the Fermionic driving field and those system operators which can change the number of Fermions within the system.

cond-mat↗
arXiv2003

The stochastic Gross-Pitaevskii equation II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al. (J. Phys. B 35,1555,(2002). The derivation does not rely on the concept of local energy and momentum conservation, and is based on a quasi-classical Wigner function representation of a "high temperature" master equation for a Bose gas, which includes only modes below an energy cutoff E_R that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provide noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation, and by the feasibility of its numerical implementation.

cond-mat↗
arXiv2002

Theory of the Ramsey spectroscopy and anomalous segregation in ultra-cold rubidium

The recent anomalous segregation experiment of Lewandowski et al. (PRL, 88, 070403, 2002) shows dramatic, rapid internal state segregation for two hyperfine levels of rubidium. We simulate an effective one dimensional model of the system for experimental parameters and find reasonable agreement with the data. The Ramsey frequency is found to be insensitive to the decoherence of the superposition, and is only equivalent to the interaction energy shift for a pure superposition. A Quantum Boltzmann equation describing collisions is derived using Quantum Kinetic Theory, taking into account the different scattering lengths of the internal states. As spin-wave experiments are likely to be attempted at lower temperatures we examine the effect of degeneracy on decoherence by considering the recent experiment of Lewandowski et al. where degeneracy is around 10%. We also find that the segregation effect is only possible when transport terms are included in the equations of motion, and that the interactions only directly alter the momentum distributions of the states. The segregation or spin wave effect is thus entirely due to coherent atomic motion as foreseen in the experimental report

cond-mat.mes-hall↗
arXiv2002

The nucleation, growth and stabilization of vortex lattices

We give a simple unified theory of vortex nucleation and vortex lattice formation which is valid from the initiation process up to the final stabilization of the lattice. We treat the growth of vortex lattices from a rotating thermal cloud, and their production using a rotating trap. We find results consistent with previous work on the critical velocity or critical angular velocity for vortex formation, and predict the initial number of vortices expected before their self assembly into a lattice. We show that the thermal cloud plays a crucial role in the process of vortex lattice nucleation.

cond-mat↗
arXiv2002

Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K. We demonstrate that within the linear response regime, both a quantum field theory treatment and a meanfield Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a meanfield formalism. We analyse the behaviour of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (meanfield, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the meanfield treatment, and can be interpreted in terms of the interference of the u and v quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.

cond-mat↗
arXiv2001

Growth of Bose-Einstein Condensates from Thermal Vapor

We report on a quantitative study of the growth process of $^{87}$Rb Bose-Einstein condensates. By continuous evaporative cooling we directly control the thermal cloud from which the condensate grows. We compare the experimental data with the results of a theoretical model based on quantum kinetic theory. We find quantitative agreement with theory for the situation of strong cooling, whereas in the weak cooling regime a distinctly different behaviour is found in the experiment.

cond-mat.soft↗
arXiv2001

Analysis of g_2 for the cold-collision frequency shift in the hydrogen condensate experiments

We compute an approximate set of longitudinal quasiparticle modes for a hydrogen condensate as produced in the MIT experiments. An expansion in quasiparticles using a simple one-dimensional Bogoliubov picture shows however that at the high temperatures (\approx 44muK) and in the very shallow trap employed (omega_z = 2π\times 10.2Hz) the contribution to the density from the quasiparticles is about 20% of that from the condensate mode, leading to an effective $ g_2(x,x) which varies between 1 and 3 depending on the position in the condensate.

cond-mat↗
arXiv2001

Theory of the cold collision frequency shift in 1S--2S spectroscopy of Bose-Einstein-condensed and non-condensed hydrogen

We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9kHz) of transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic "foot" extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.

cond-mat↗
arXiv2000

Quantum kinetic theory VII: The influence of vapor dynamics on condensate growth

We extend earlier models of the growth of a Bose-Einstein condensate to include the full dynamical effects of the thermal cloud by numerically solving a modified quantum Boltzmann equation. We determine the regime in which the assumptions of the simple model are a reasonable approximation, and compare our new results with those that were earlier compared with experimental data. We find good agreement with our earlier modelling, except at higher condensate fractions, for which a significant speedup is found. We also investigate the effect of temperature on condensate growth, and find that this has a surprisingly small effect. The discrepancy between theory and experiment remains, since the speedup found in these computations does not occur in the parameter regime specified in the the experiment.

cond-mat↗
arXiv1999

Quantum Kinetic Theory VI: The Growth of a Bose-Einstein Condensate

A detailed analysis of the growth of a BEC is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modelling of growth implicitly gives a model of the spatial shape of the condensate vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi shaped condensate. Our method may give substantially different results for condensate numbers and temperatures obtained from phenomentological fits, and indicates the need for more systematic investigation of the growth dynamics of the condensate from a supersaturated vapor.

cond-mat↗
arXiv1999

Evaluation of heating effects on atoms trapped in an optical trap

We solve a stochastic master equation based on the theory of Savard et al. [T.A. Savard, K.M. O'Hara and J.E. Thomas, Phys. Rev. A 56, R1095 (1997)] for heating arising from fluctuations in the trapping laser intensity. We compare with recent experiments of Ye et. al. [J. Ye, D.W. Vernooy and H.J. Kimble, Trapping of single atoms in cavity QED, quant-ph/9908007, Phys. Rev. Lett. (1999 in press)], and find good agreement with the experimental measurements of the distribution of trap occupancy times. The major cause of trap loss arises from the broadening of the energy distribution of the trapped atom, rather than the mean heating rate, which is a very much smaller effect.

quant-ph↗
arXiv1999

Dressed States of a two component Bose-Einstein Condensate

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.

cond-mat↗
arXiv1998

Entanglement of atoms via cold controlled collisions

We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum--gates and efficient creation of highly entangled states of many atoms in optical lattices.

quant-ph↗
arXiv1998

Cold bosonic atoms in optical lattices

The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.

cond-mat.stat-mech↗
arXiv1998

Quantum Kinetic Theory of Condensate Growth---Comparison of Experiment and Theory

In a major extension of our previous model (C.W. Gardiner, P. Zoller, R.J. Ballagh and M.J. Davis, Phys. Rev. Lett. 79, 1793 (1997)) of condensate growth, we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels. We find good agreement with experiment, especially at higher temperatures. We also confirm the picture of the ``kinetic'' region of evolution, introduced by Kagan et al, for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient W^{+}.

cond-mat↗
arXiv1998

Quantum kinetic theory IV: Intensity and amplitude fluctuations of a Bose- Einstein condensate at finite temperature including trap loss

We use the quantum kinetic theory to calculate the steady state and the fluctuations of a trapped Bose-Einstein condensate at finite temperature. The system is divided in a condensate and a non-condensate part. A quantum mechanical description based on the number conserving Bogoliubov method is used for describing the condensate part. The non-condensed particles are treated as a classical gas in thermal equilibrium with temperature T and chemical potential mu. We find a master equation for the reduced density operator of the Bose-Einstein condensate, calculate the steady state of the system and investigate the effect of one- two- and three particle loss on the condensate. Using linearized Ito equations we find expressions for the intensity fluctuations and the amplitude fluctuations in the condensate. A Lorentzian line shape is found for the intensity correlation function that is characterized by a time constant gammaI^(-1) derived in the paper. For the amplitude correlation function we find ballistic behavior for time differences smaller than gammaI^(-1) and diffusive behavior for larger time differences

cond-mat.stat-mech↗