We discuss BEC in (quasi)2D trapped gases and find that well below the transition temperature Tc the equilibrium state is a true condensate, whereas at intermediate temperatures T < Tc one has a quasicondensate (condensate with fluctuating phase). The mean-field interaction in a quasi2D gas is sensitive to the frequency ω0 of the (tight) confinement in the "frozen" direction, and one can switch the sign of the interaction by changing ω0. Variation of ω0 can also reduce the rates of inelastic processes. This offers promising prospects for tunable BEC in trapped quasi2D gases. 03.75.Fi,05.30.Jp The influence of dimensionality of the system of bosons on the presence and character of Bose-Einstein condensation (BEC) and superfluid phase transition has been a subject of extensive studies in spatially homogeneous systems. In 2D a true condensate can only exist at T = 0, and its absence at finite temperatures follows from the Bogolyubov k −2 theorem and originates from long-wave fluctuations of the phase (see, e.g., [1,2]). However, as was first pointed out by Kane and Kadanoff [3] and then proved by Berezinskii [4], there is a superfluid phase transition at sufficiently low T . Kosterlitz and Thouless [5] found that this transition is associated with the formation of bound pairs of vortices below the critical temperature T KT = (πh 2 /2m)n s (m is the atom mass, and n s the superfluid density just below T KT ). Earlier theoretical studies of 2D systems have been reviewed in [2] and have led to the conclusion that below the KosterlitzThouless Transition (KTT) temperature the Bose liquid (gas) is characterized by the presence of a quasicondensate, that is a condensate with fluctuating phase (see [6]). In this case the system can be divided into blocks with a characteristic size greatly exceeding the healing length but smaller than the radius of phase fluctuations. Then, there is a true condensate in each block but the phases of different blocks are not correlated with each other.The KTT has been observed in monolayers of liquid helium [7]. The only dilute atomic system studied thus far was a 2D gas of spin-polarized atomic hydrogen on liquid-helium surface (see [8] for review). Recently, the observation of KTT in this system has been reported [9].BEC in trapped 2D gases is expected to be qualitatively different. The trapping potential introduces a finite size of the sample, which sets a lower bound for the momentum of excitations and reduces the phase fluctuations. Moreover, for an ideal 2D Bose gas in a harmonic potential Bagnato and Kleppner [10] found a macroscopic occupation of the ground state of the trap (ordinary BEC) at temperatures T < T c ≈ N 1/2h ω, where N is the number of particles, and ω the trap frequency. Thus, there is a question of whether an interacting trapped 2D gas supports the ordinary BEC or the KTT type of a cross-over to the BEC regime [11]. However, the critical temperature will be always comparable with T c of an ideal gas: On approaching T c from above, the gas density is n c ∼ N/R 2 Tc ...

We show that the critical temperature of a uniform dilute Bose gas increases linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations.Determination of the effect of repulsive interactions on the transition temperature of a homogeneous dilute Bose gas at fixed density has had a long and controversial history [1][2][3][4][5]. While [1] predicted that the first change in the transition temperature, T c , is of order the scattering length a for the interaction between the particles, neither the sign of the effect nor its dependence on a has been obvious. Recent renormalization group studies [4] predict an increase of the critical temperature. Numerical calculations by Grüter, Ceperley, and Laloë [6], and more recently by Holzmann and Krauth [7], of the effect of interactions on the Bose-Einstein condensation transition in a uniform gas of hard sphere bosons, and approximate analytic calculations by Holzmann, Grüter, and Laloë of the dilute limit [8], have shown that the transition temperature, T c , initially rises linearly with a. The effect arises physically from the change in the energy of low momentum particles near T c [8]. Here we analyze the leading order behavior of diagrammatic perturbation theory, and argue that T c increases linearly with a. We then construct an approximate self-consistent solution of the single particle spectrum at T c which demonstrates the change in the low momentum spectrum, and which enables us to calculate the change in T c quantitatively.We consider a uniform system of identical bosons of mass m, at temperature T close to T c and use finite temperature quantum many-body perturbation theory. We assume that the range of the two-body potential is small compared to the interparticle distance n −1/3 , so that the potential can be taken to act locally and be characterized entirely by the s-wave scattering length a. Thus we work in the limit a ≪ λ, where λ = 2πh 2 /mk B T 1/2 is the thermal wavelength. (We generally use units h = k B = 1.)To compute the effects of the interactions on T c , we write the density n as a sum over Matsubara frequencies ω ν = 2πiνT (ν = 0, ±1, ±2, . . .) of the single particle Green's function, G(k,z):wherewith µ the chemical potential. The Bose-Einstein condensation transition is determined by the point where G −1 (0, 0) = 0, i.e., where Σ(0, 0) = µ. The first effect of interactions on Σ is a mean field term Σ mf = 2gn, where g = 4πh 2 a/m; the factor of two comes from including the exchange term. Such a contribution, independent of k and z has no effect on the transition temperature, as it can be simply absorbed in a redef...

We discuss the origin of the finite-size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random-phase approximation at long wavelengths. The correction is determined mainly by the collective charge oscillations of the interacting system. Finite-size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.

We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well-described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.Long-range coherence is the hallmark of superfluidity and Bose-Einstein condensation [1,2]. The character of spatial coherence in a system and the properties of the corresponding phase transitions are fundamentally influenced by dimensionality. The two-dimensional case is particularly intriguing as for a homogeneous system, true long-range order cannot persist at any finite temperature due to the dominant role of phase fluctuations with large wavelengths [3][4][5]. Although this prevents Bose-Einstein condensation in 2D, a transition to a superfluid phase with quasi-long-range order can still occur, as pointed out by Berezinskii, Kosterlitz, and Thouless (BKT) [6][7][8]. A key prediction of this theory is the scale-invariant behavior of the first-order correlation function g 1 (r), which, in the low-temperature phase, decays algebraically according to g 1 (r) ∝ r −η for large separations r. Importantly, the BKT theory for homogeneous systems predicts a universal value of η c = 1/4 at the critical temperature, accompanied by a universal jump of the superfluid density [9].Several key signatures of BKT physics have been experimentally observed in a variety of systems such as exciton-polariton condensates [10], layered magnets [11,12], liquid 4 He films [13], and trapped Bose gases [14][15][16][17][18][19][20]. Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13]. More recently, in the pioneering interference experiment with a weakly interacting Bose gas [14], the emergence of quasi-long-range order and the proliferation of vortices were shown.There are still important aspects of superfluidity in two-dimensional systems that remain to be understood, which we aim to elucidate in this work with ultracold atoms. One question is whether the BKT phenomenology can also be extended to systems with nonuniform density. Indeed, if the microscopic symmetries are the same, the general physical picture involving phase fluctuations should be valid also for inhomogeneous systems. However, it ...

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates.

We present a Monte Carlo calculation for up to N ∼ 20 000 bosons in 3 D to determine the shift of the transition temperature due to small interactions a. We generate independent configurations of the ideal gas. At finite N , the superfluid density changes by a certain correlation function in the limit a → 0; the N → ∞ limit is taken afterwards. We argue that our result is independent of the order of limits. Detailed knowledge of the non-interacting system for finite N allows us to avoid finite-size scaling assumptions. PACS numbers: 03.75. Fi, 02.70.Lq, 05.30.Jp Feynman [1] has provided us with a classic formula for the partition function of the canonical noninteracting Bose gas. It represents a "path-integral without paths", as they have been integrated out. What remains is the memory of the cyclic structure of the permutations that were needed to satisfy bosonic statistics:The partitions {m k } in eq.(1) decompose permutations of the N particles into exchange cycles (m i cycles of length i for all 1 ≤ i ≤ N with k k m k = N ). ρ k is a system-dependent weight for cycles of length k.In this paper we present an explicit Monte Carlo calculation for up to ∼ 20 000 bosons in three dimensions, starting from eq. (1). The calculation allows us to determine unambiguously the shift in the transition temperature T c for weakly interacting bosons in the thermodynamic limit for an infinitesimal s-wave scattering length a. This fundamental question has lead to quite a number of different and contradictory theoretical as well as computational answers (cf, e.g., [2][3][4]).We will first use Eq. (1) and its generalizations to determine very detailed properties of the finite-N canonical Bose gas in a box with periodic boundary conditions. We then point out that all information on the shift of T c for weakly interacting gases is already contained in the noninteracting system. In the linear response regime (infinitesimal interaction), it is a certain correlation function of the noninteracting system which determines the shift in T c . This correlation is much too complicated to be calculated directly, but we can sample it, even for very large N . To do so, we generate independent bosonic configurations in the canonical ensemble. We have found a solution (based on Feynman's formula Eq. (1)) which avoids Markov chain Monte Carlo methods. In our twostep procedure, a partition {m k } is generated with the correct probability P({m k }). Then, a random boson configuration is constructed for the given partition.We stress that all our calculations are done very close to T c , so that the correlation length ξ of any macroscopic sample is much larger than the actual system size L of the simulation. This condition L ≪ ξ allows us to invoke the standard finite-size scaling hypothesis [5], but also to take the N → ∞ limit after the limit a → 0.A key concept in the path integral representation of bosons is that of a winding number. Consider first the density matrix ρ(r, r ′ , β) of a single particle [r = (x, y, z)] at inverse temperature β ...

The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron-ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25-30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.high pressure | phase transitions | quantum Monte Carlo | hydrogen metallization | molecular dissociation H ydrogen is the simplest element of the periodic table and a paradigmatic element in developing general physical theories of condensed matter. Despite the simple electronic structure, its phase diagram is unexpectedly rich, ranging from the normal three-phase equilibria (solid-liquid-gas) of the lowpressure molecular system to the fully dissociated and ionized plasma states at extreme conditions of temperature and pressure. Accurate knowledge of its phase diagram is highly relevant as testified by the continuing intense research activity over the last half century (1-5). Its relevance in nature arises because it is the most abundant element in the universe and, together with the next simplest element helium, constitutes 70-90% of the atmosphere of the giant planets, Jupiter and Saturn, and of the many, recently discovered, exoplanets. Also, it is the putative element for nuclear fusion for energy applications.The longest outstanding issue concerns the metal-insulator transition and its interplay with molecular dissociation. Molecular dissociation can occur either upon increasing temperature in the low-pressure fluid or upon increasing pressure in the low-temperature crystalline phase, or even as a combined action of temperature and pressure in the denser molecular fluid (5). The first prediction of metallization at zero temperature suggested that the molecular crystal would become atomic and transform to a simple metal above 25 GPa (1). Later experiments with higher pressures up to at least 360 GPa have found no convincing evidence of the metallic state at least below room temperature. However, they have revealed a rich phase diagram with a sequence of phase transformations in the molecular solid and the possibility of a semimetallic state (3, 6-13).The metallic state has been unequivocally observed in the dense fluid in the range of 100-200 GPa and estimated temperatures of 2,000-3,000 K by dynamical compression experiments (5, 14-16). Using the ...

We justify and evaluate backflow three-body wave functions for a two-component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wave functions are used in variational and diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-three-body wave functions lead to energies nearly as low as those from using local density approximation orbitals in the trial wave function. However, compared to wave functions constructed from density functional solutions, backflow wave functions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.