Bose-Einstein Condensation Phase Research Articles

Multiple Magnon Modes and Consequences for the Bose-Einstein Condensed Phase inBaCuSi2O6

The compound BaCuSi2O6 is a quantum magnet with antiferromagnetic dimers of S=1/2 moments on a quasi-2D square lattice. We have investigated its spin dynamics by inelastic neutron scattering experiments on single crystals with an energy resolution considerably higher than in an earlier study. We observe multiple magnon modes, indicating clearly the presence of magnetically inequivalent dimer sites. The more complex spin Hamiltonian revealed in our study leads to a distinct form of magnon Bose-Einstein condensate phase with a spatially modulated condensate amplitude.

Diquark Bose–Einstein condensation and nuclear matter

We study a possible transition between symmetric nuclear matter and the diquark Bose–Einstein condensate (BEC) matter at zero temperature. We find that chiral restoration transition is first order and coincides with deconfinement. We investigate various possible coexistence patterns which may emerge from the first order deconfinement phase transition by assuming different values for the critical deconfinement chemical potential. If deconfinement takes place at higher chemical potential, there exists a mixed phase of nuclear and chirally restored diquark BEC matter. This coexistence region extends over a large density region for a bigger diquark BEC or a weaker diquark–diquark interaction. For model parameters with heavy diquark in vacuum, phase transition to diquark matter becomes of second-order. We also show that in the case of precocious deconfinement, droplets of nucleons and droplets of chirally restored Bose–Einstein condensed diquarks coexist surrounded by non-trivial vacuum. We show that a early deconfinement and a weak repulsive diquark–diquark interaction soften the equation of state. We propose a scenario in which nuclear matter saturates due to the formation of the diquark BEC and deconfinement phenomena. In this picture, instead of repulsive vector-meson exchange the compressibility of the equation of state is related to a repulsive diquark–diquark interaction. In general, we emphasize the importance of a diquark BEC phase at rather low density before quark BCS-pairing transition.

Quantum Criticality in an Organic Magnet

Exchange interactions between S=1/2 sites in piperazinium hexachlorodicuprate produce a frustrated bilayer magnet with a singlet ground state. We have determined the field-temperature phase diagram by high field magnetization and neutron scattering experiments. There are two quantum critical points: Hc1=7.5 T separates a quantum paramagnet phase from a three dimensional, antiferromagnetically ordered state while Hc2=37 marks the onset of a fully polarized state. The ordered phase, which we describe as a magnon Bose-Einstein condensate (BEC), is embedded in a quantum critical regime with short range correlations. A low temperature anomaly in the BEC phase boundary indicates that additional low energy features of the material become important near Hc1.

Probing BEC phase fluctuations with atomic quantum dots

We consider the dephasing of two internal states |0⟩ and |1⟩ of a trapped impurity atom, a so-called atomic quantum dot (AQD), where only state |1⟩ couples to a Bose–Einstein condensate (BEC). A direct relation between the dephasing of the internal states of the AQD and the temporal phase fluctuations of the BEC is established. Based on this relation we suggest a scheme to probe BEC phase fluctuations non-destructively via dephasing measurements of the AQD. In particular, the scheme allows to trace the dependence of the phase fluctuations on the trapping geometry of the BEC.

Zero-Temperature Phases of Many-Atom Bose Systems

We show that a many-atom Bose system at zero temperature has, in general, a liquid phase in addition to its well-known gaseous phase. A universal phase diagram is presented that is applicable to all Bose systems with a -C6/r6 type of interaction at large interparticle separations. We show that the predicted phase structure has implications on the stability of a gaseous Bose-Einstein condensate (BEC) even at dilute densities that are routinely achieved under existing experimental conditions. We also predict that should have a gaseous BEC phase below a critical density of 5.58 x 10(15) 1/cm3.

Diagnostics for the ground-state phase of a spin-2 Bose-Einstein condensate

We propose a method to determine the singlet-pair energy of a spin-2 Bose-Einstein condensate (BEC). By preparing the initial populations in the magnetic sublevels 0, 2, -2 with appropriate relative phases, we can obtain the coefficient of the spin singlet-pair term from the spin exchange dynamics. This method is suitable for hyperfine states with short lifetimes, since only the initial change in the population of each magnetic sublevel is needed. This method therefore enables the determination of the ground state phase of a spin-2 87Rb BEC at zero magnetic field, which is considered to lie in the immediate vicinity of the boundary between the antiferromagnetic and cyclic phases. We also show that the initial state in which relative phases are controlled can be prepared by Raman processes.

Random phases in Bose-Einstein condensates with higher order nonlinearities

We present a statistical description of Bose-Einstein condensates with general higher order nonlinearities. In particular, we investigate the case of cubic-quintic nonlinearities, of particular interest for dilute condensates. The implication of decoherence for the stability properties of the condensate is discussed.

Absence of Single-Particle Bose-Einstein Condensation at Low Densities for Bosons with Correlated Hopping

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.

Atomic Gases at Negative Kinetic Temperature

We show that thermalization of the motion of atoms at negative temperature is possible in an optical lattice, for conditions that are feasible in current experiments. We present a method for reversibly inverting the temperature of a trapped gas. Moreover, a negative-temperature ensemble can be cooled (reducing |T|) by evaporation of the lowest-energy particles. This enables the attainment of the Bose-Einstein condensation phase transition at negative temperature.

On superflow in solidHe4

Kim and Chan have recently observed Non-Classical Rotational Inertia (NCRI) for solid $^4$He in Vycor glass, gold film, and bulk. Their low $T$ value of the superfluid fraction, $\rho_{s}/\rho\approx0.015$, is consistent with what is known of the atomic delocalization in this quantum solid. By including a lattice mass density $\rho_{L}$ distinct from the normal fluid density $\rho_{n}$, we argue that $\rho_{s}(T)\approx\rho_{s}(0)-\rho_{n}(T)$, and we develop a model for the normal fluid density $\rho_{n}$ with contributions from longitudinal phonons and ``defectons'' (which dominate). The Bose-Einstein Condensation (BEC) and macroscopic phase inferred from NCRI implies quantum vortex lines and quantum vortex rings, which may explain the unusually low critical velocity and certain hysteretic phenomena.

Bose-Einstein quantum phase transition in an optical lattice model

Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomenon which we are able to analyze rigorously. The system is a hard core lattice gas at half-filling and the optical lattice is modeled by a periodic potential of strength $\lambda$. For small $\lambda$ and temperature, BEC is proved to occur, while at large $\lambda$ or temperature there is no BEC. At large $\lambda$ the low-temperature states are in a Mott insulator phase with a characteristic gap that is absent in the BEC phase. The interparticle interaction is essential for this transition, which occurs even in the ground state. Surprisingly, the condensation is always into the $p=0$ mode in this model, although the density itself has the periodicity of the imposed potential.

Erratum: Polarizability, correlation energy, and dielectric liquid phase of Bose-Einstein condensate of two-dimensional excitons in a strong perpendicular magnetic field [Phys. Rev. B66, 245316 (2002)

Erratum: Polarizability, correlation energy, and dielectric liquid phase of Bose-Einstein condensate of two-dimensional excitons in a strong perpendicular magnetic field [Phys. Rev. B<b>66</b>, 245316 (2002)

Detecting supercounterfluidity by Ramsey spectroscopy

A two-component system of ultracold atoms in an optical lattice at integer total filling factor and strong enough onsite repulsion can form a supercounterfluid (SCF) phase, which can be viewed as the Bose-Einstein condensate (BEC) of pairs formed by particles of one sort and holes of another sort. In this quasimolecular BEC, no single-component BEC exists, and the net atomic flow is prohibited. We show that, in the case of the interconvertible species (like hyperfine states of Rb), the corresponding order parameter can be detected by spatially selective Ramsey spectroscopy. The method can be used, in particular, for revealing a persistent supercounterflow as well as the SCF vortices---imposing a single $\ensuremath{\pi}/2$ rf-pulse will result in a specific phase-separation pattern. The detection of the SCF should be considered in conjunction with observing no typical BEC interference fringes for each component. The consequences of the strong SCF correlations persistent in the two atomic BECs phase are discussed as well.

Meissner effect in a charged Bose gas with short-range repulsion

The question of whether the Bose-Einstein condensate (BEC) is a necessary condition of the Meissner effect is examined. The electromagnetic susceptibility of a charged Bose gas with short-range repulsion is studied using the perturbation theory with respect to the repulsive force. With decreasing temperature, the Bose-statistical coherence grows, and prior to the BEC phase the susceptibility shows a singularity implying the Meissner effect. This means that the BEC is a sufficient, but not a necessary, condition of the Meissner effect in the charged Bose gas with short-range repulsion.

Generation of maximally entangled states of a Bose-Einstein condensate and Heisenberg-limited phase resolution

We outline a procedure for Heisenberg-limited phase resolution between two Bose-Einstien condensates (BECs) defined as different hyperfine levels. The method involves first establishing a maximally entangled state using the ideas of nonlinear interferometry previously discussed in the optical domain [C. C. Gerry et al., Phys. Rev. A 66, 013804 (2002)]. In the case of the condensates, the nonlinear interactions are realized by the interatomic interactions within each condensate. Quarter cycle Raman pulses between hyperfine levels act as beam splitters. Parity measurements of one of the components of the BEC resolve the phase at the Heisenberg limit. We point out that parity measurements can be made by coupling the mode of interest with a third condensate where both components evolve under nonlinear interatomic interactions. After another Raman pulse, the components are populated according to parity. One need only determine which component is populated to determine the parity.

Polarizability, correlation energy, and dielectric liquid phase of Bose-Einstein condensate of two-dimensional excitons in a strong perpendicular magnetic field

The coherent pairing of electrons and holes occupying only the lowest Landau level in a two-dimensional (2D) system with a strong perpendicular magnetic field is studied using the Keldysh-Kozlov-Kopaev method and generalized random phase approximation. Bose-Einstein condensation of the correlated pairs takes place in a single particle state with an arbitrary wave vector $\mathbf{k}$ in a symmetric 2D model. We show that the ground state energy per exciton and the chemical potential are nonmonotonic functions of the filling factor, so that metastable dielectric liquid states with positive compressibility exist, consisting of Bose-Einstein condensate of magnetoexcitons. It is shown that this dielectric liquid phase of the Bose condensed excitons is more stable than the metallic electron-hole liquid phase. The polarizability of the Bose-condensed magnetoexcitons is calculated using Anderson-type wave functions of the coherent excited states, which correspond to the appearance of one out-of-condensate electron-hole $(e\ensuremath{-}h)$ pair in the presence of the BCS-type ground state. The polarizability is characterized by a coherent factor which depends on $\mathbf{k}$ and vanishes when $\mathbf{k}$ tends to zero, as well as by a resonance frequency equal to the ionization potential of a magnetoexciton, and differs considerably from the polarizability of a noncondensed exciton gas. The condensate polarizability is used to determine the correlation energy of the system and the correction to the chemical potential beyond the Hartree-Fock-Bogoliubov approximation.

Spontaneous Bose coherence of excitons and polaritons.

In the past decade, there has been an increasing number of experiments on spontaneous Bose coherence of excitons and polaritons. Four major areas of research are reviewed here: three-dimensional excitons in the bulk semiconductor Cu2O, two-dimensional excitons in coupled quantum wells, Coulomb drag experiments in coupled two-dimensional electron gases, and polaritons in semiconductor microcavities. The unifying theory of all these experiments is the effect of spontaneous symmetry breaking in the Bose-Einstein condensation phase transition.

Bose-Einstein condensation and long-range phase coherence in the many-particle Schrödinger wave function

The properties of the many-particle Schr\"odinger wave function \ensuremath{\Psi} are examined in the presence of Bose-Einstein condensation (BEC). It is shown that it is possible to define, in terms of \ensuremath{\Psi}, a function $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s}),$ which can be regarded as the single-particle wave function of an arbitrary particle for a fixed configuration $\stackrel{\ensuremath{\rightarrow}}{s}$ of all other particles. It is shown that $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ plays an analogous role to the field operator of standard field-theoretical treatments of superfluidity. It is shown that in the presence of a Bose-Einstein condensate fraction f, $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ must be nonzero and phase coherent within at least a fraction f of the total volume of the N-particle system for essentially all $\stackrel{\ensuremath{\rightarrow}}{s}.$ Examination of the form of variational many-particle wave functions shows that in liquid ${}^{4}\mathrm{He},$ $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ extends throughout the spaces left between the hard cores of the other atoms at $\stackrel{\ensuremath{\rightarrow}}{s}.$ By contrast, in the absence of BEC, $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ in the ground state must be nonzero only over a localized region of space. It is shown that in order for long-range phase coherence in $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ to be maintained in the presence of velocity fields, any circulation must be quantized over macroscopic length scales. Some numerical calculations of the properties and fluctuations of liquid helium are presented. These suggest that the approach outlined in this paper may have significant advantages for the numerical calculations of the properties of Bose-Einstein condensed systems. The properties of $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ are used to show that there is no general connection between the static structure factor and the size of the Bose-Einstein condensate fraction in a Bose fluid. It is suggested that the observed connection in liquid ${}^{4}\mathrm{He}$ is due to the creation of vacancies in the liquid structure, which are required so that $\ensuremath{\psi}(\stackrel{\ensuremath{\rightarrow}}{r}|\stackrel{\ensuremath{\rightarrow}}{s})$ can delocalize, in the presence of hard-core interactions. It is shown that this suggestion is quantitatively consistent with observations on liquid ${}^{4}\mathrm{He}.$ It is suggested that the superfluid transition in ${}^{4}\mathrm{He}$ occurs when the vacancies in the liquid structure form a connected network.

Finite-size scaling and the role of the thermodynamic ensemble in thetransition temperature of a dilute Bose gas

We study the Bose-Einstein condensation phase transition in a weaklyinteracting gas through a perturbative analysis of finite systems. In boththe grand canonical and the canonical ensembles, perturbation theorysuffers from infrared divergences and cannot directly determine thetransition temperature in the thermodynamic limit. However, inconjunction with finite-size scaling, perturbation theory provides apowerful calculation tool. Here we use this combinationof perturbation theory and scalingto estimate a shift in the transition temperature in thecanonical ensemble consistent with grand canonicalcalculations.

Classification of phase transitions of finite Bose-Einstein condensates in power-law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.