Sub-Poissonian fluctuations in a 1D Bose gas: from the quantum quasicondensate to the strongly interacting regime

We report on local, in situ measurements of atom number fluctuations in slices of a one-dimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super- to sub-Poissonian as the density is increased, which is a signature of the transition between the subregimes where the two-body correlation function is dominated, respectively, by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to sub-Poissonian, as expected for a "fermionized" gas.     

Definition and measurement of global thermodynamic variables for laser-cooled trapped gas

We have used the definition of global thermodynamic variables like pressure and volume for atoms trapped in a nonuniform potential to measure the state equation for a sample of cold Na atoms kept trapped in a quadrupole magnetic field. The results show that, for low atomic density, the system behaves like an ideal gas where pressure and volume are inversely proportional. At high density values (compressed system), the deviation from an ideal gas is clear. A model based on virial expansion shows that the measured deviation is larger than the expected first-order correction. Employing the concept of global variables may be an important procedure to describe the thermodynamic of gases in the ultracold regime eventually crossing the values where critical phenomena like Bose condensation, among others, take place.     

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (T_c) the Casimir force for this non-interacting system decreases with temperature (T) and at , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.     

Thermodynamic properties of a rotating Bose gas in harmonic trap

In this paper, the thermodynamic properties of a rotating Bose gas in harmonic trap are investigated. In particularly, the condensate fraction, critical temperature and heat capacity are analytically calculated. A simple semiclassical approximation, which is the density of state approach, is suggested. This approach is able to include the effects, such as the finite size and the chemical potential when becomes equal to the energy of the lowest energy state, that altered the rotating ideal Bose gas simultaneously. The calculated results show that the thermodynamic properties depend strongly on the rotation rate. The rapid rotation leads to a highly anisotropic confinement potential. The possibility for dimensionality cross-over to lower dimensions for this system is discussed. We compare the outcome results with the experimental measured data of Coddington et al. [Phys. Rev. A 70, 063607 (2004)].     

Probing three-body correlations in a quantum gas using the measurement of the third moment of density fluctuations

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.     

Bosonization, pairing, and superconductivity of the fermionic Tonks-Girardeau gas

We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that its two-particle reduced density matrix exhibits superconductive off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement, we show that during an expansion the momentum distribution undergoes a "dynamical bosonization," approaching that of an ideal Bose gas without violating the Pauli exclusion principle.     

Critical point of an interacting two-dimensional atomic Bose gas

We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.     

Critical behaviour of a relativistic ideal Bose gas with pair production

We discuss the critical behaviour of an ideal relativistic Bose gas (in d dimensions) with a net charge including the effects of pair production. We show that the critical exponents of the system are the same as those of the usual nonrelativistic Bose gas. The universal ratios formed from the critical amplitude are also the same as those of the usual Bose gas.     

Scaling behaviour in the Bose gas

The scaling behaviour of fluctuations of the Bose field (f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators (f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.     

Dynamical transition from a quasi-one-dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

We analyze in detail the expansion of a 1D Bose gas after removing the axial confinement. We show that during its one-dimensional expansion the density of the Bose gas does not follow a self-similar solution. Our analysis is based on a nonlinear Schr?dinger equation with variable nonlinearity whose validity is discussed for the expansion problem, by comparing with an exact Bose-Fermi mapping for the case of an initial Tonks-Girardeau gas. For this case, the gas is shown to expand self-similarly, with a different scaling law compared to the one-dimensional Thomas-Fermi condensate.     

Study of weakly interacting trapped Bose gas

We have obtained expressions for single particle density and two particle density ofweakly interacting trapped quantum gases. These are valid for all temperature and in anydimension. These expressions have been simplified and expressed in terms ofnon-interacting single particle density. The ground fluctuations for T<T_cin grand canonical ensemble has been treated with care using the method of Kocharovskyet al. [Phys. Rev. A 61, 053606 (2000)]. Some numerical results are presentedin one and three dimension for isotropic harmonically trapped Bose gas with contactinteractions. It is seen that boson density decreases with increasing repulsiveinteractions. The expression for critical temperature is also shown to agree with earlierresult and is in accordance with experiments.     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

BEC transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount DeltaT(c) approximately equal to ca(sc)n(1/3)T(0) from the ideal gas result T(0), where a(sc) is the scattering length, n is the density, and c is a pure number. There have been several different theoretical estimates for c. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) straight phi(4) field theory in three dimensions-an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce nonuniversal quantities such as the critical temperature. We find c = 1.32+/-0.02.     

Theory of a weakly nonideal Bose gas in a magnetic field

This paper investigates Bose-Einstein condensation of an ideal gas of finite-spin bosons in an external magnetic field. We generalize Bogolyubov’s theory of a weakly nonideal Bose gas to the case where the gas of finite-spin bosons is located in an external magnetic field. We find the corresponding quasiparticle spectrum and formulate the superfluidity criterion for the boson gas. The magnetization of the weakly nonideal Bose gas is also determined. Finally, we specify a method of studying kinetic processes that take place in a weakly nonideal Bose gas. Zh. éksp. Teor. Fiz. 113, 918–929 (March 1998)     

Transition temperatures of the trapped ideal spinor Bose gas

The thermodynamic properties of the trapped ideal spinor Bose gas are studied in details with the constraints of fixed total number of atoms N, and magnetization M. The double transition temperatures, their corresponding corrections due to finite particle number, and the population of each component are investigated. The generalization to the ideal spinor Bose gas of hyperfine quantum number F is also discussed. We propose that the order and disorder parameters to describe the symmetry broken of condensation.     

Quantized vortices in the ideal bose gas: a physical realization of random polynomials

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.     

Observation of anomalous spin segregation in a trapped Fermi gas

We report the observation of spin segregation, i.e., time-dependent separation of the spin density profiles of two spin states, in a trapped, coherently prepared Fermi gas of 6Li with a magnetically tunable scattering length a12 close to zero. For |a12| approximately = 5 bohr, as the cloud profiles evolve, the measured difference in the densities at the cloud center increases in 200 ms from 0 to approximately = 60% of the initial mean density and changes sign with a12. The data are in disagreement in both amplitude and temporal evolution with a spin-wave theory for a Fermi gas. In contrast, for a Bose gas, an analogous theory has successfully described previous observations of spin segregation. The observed segregated atomic density profiles are far from equilibrium, yet they persist for approximately = 5 s, long compared to the axial trapping period of 6.9 ms. We find the zero crossing in a12=0, where spin segregation ceases, at 527.5+/-0.2 G.     

Universality of the one-dimensional Bose gas with delta interaction

We consider several models of interacting bosons in a one-dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta interaction. The lattice corrections corresponding to the different models are contrasted.     

Impurity-induced phase transition in the interacting Bose gas: 1. Analytical results

We derive selfconsistency equations for the density relaxation and the longitudinal dynamical conductivity of the interacting Bose gas at temperature zero moving in a random potential. The equations describe a disorder-induced transition from a superfluid phase to an insulating phase, where the density is non-ergodic. The interaction of the bosons is treated in random phase approximation and the coupling to the impurities is calculated within generalized selfconsistent current relaxation theory. Scaling laws are discussed and explicit results are presented for the repulsive Bosgas with neutral impurities and for the charged Bose gas with charged impurities.     

Direct observation of sub-Poissonian number statistics in a degenerate bose gas

We report the direct observation of sub-Poissonian number fluctuation for a degenerate Bose gas confined in an optical trap. Reduction of number fluctuations below the Poissonian limit is observed for average numbers that range from 300 to 60 atoms.