Critical Temperature For Bose-Einstein Condensation Research Articles

Searching for Unconventional Superfluid in Excitons of Monolayer Semiconductors.

It is well known that two-dimensional (2D) bosons in homogeneous space cannot undergo real Bose-Einstein condensation, and the superfluid to normal phase transition is Berezinskii-Kosterlitz-Thouless (BKT) type, associated with vortex-antivortex pair unbinding. Here we point out a 2D bosonic system whose low energy physics goes beyond conventional paradigm of 2D homogeneous bosons, i.e., intralayer excitons in monolayer transition metal dichalcogenides. With intrinsic valley-orbit coupling and valley Zeeman energy, exciton dispersion becomes linear at small momentum, giving rise to a series of novel features. The critical temperature of Bose-Einstein condensation of these excitons is nonzero, suggesting true long-range order in 2D homogeneous system. The dispersion of Goldstone mode at long wavelength has the form ϵ(q)∼sqrt[q], in contrast to conventional linear phonon spectrum. The vortex energy deviates from the usual logarithmic form with respect to system size, but instead has an additional linear term. Superfluid to normal phase transition is no longer BKT type for system size beyond a characteristic scale, without discontinuous jump in superfluid density. With the recent experimental progress on exciton fluid at thermal equilibrium in monolayer semiconductors, our work points out an experimentally accessible system to search for unconventional 2D superfluids beyond BKT paradigm.

Quantum Bubbles in Microgravity.

The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate self-interferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum MonteCarlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.

Momentum Distribution in the Unitary Bose Gas from First Principles

We consider a realistic bosonic N-particle model with unitary interactions relevant for Efimov physics. Using quantum MonteCarlo methods, we find that the critical temperature for Bose-Einstein condensation is decreased with respect to the ideal Bose gas. We also determine the full momentum distribution of the gas, including its universal asymptotic behavior, and compare this crucial observable to recent experimental data. Similar to the experiments with different atomic species, differentiated solely by a three-body length scale, our model only depends on a single parameter. We establish a weak influence of this parameter on physical observables. In current experiments, the thermodynamic instability of our model from the atomic gas towards an Efimov liquid could be masked by the dynamical instability due to three-body losses.

Competition between Bose-Einstein Condensation and Spin Dynamics.

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

Creation and counting of defects in a temperature-quenched Bose-Einstein condensate

We study the spontaneous formation of defects in the order parameter of a trapped ultracold bosonic gas while crossing the critical temperature for Bose-Einstein Condensation (BEC) at different rates. The system has the shape of an elongated ellipsoid, whose transverse width can be varied to explore dimensionality effects. For slow enough temperature quenches we find a power-law scaling of the average defect number with the quench rate, as predicted by the Kibble-Zurek mechanism. A breakdown of such a scaling is found for fast quenches, leading to a saturation of the average defect number. We suggest an explanation for this saturation in terms of the mutual interactions among defects.

Quantum Enhancement of the Index of Refraction in a Bose-Einstein Condensate.

We study the index of refraction of an ultracold bosonic gas in the dilute regime. Using phase-contrast imaging with light detuned from resonance by several tens of linewidths, we image a single cloud of ultracold atoms for 100 consecutive shots, which enables the study of the scattering rate as a function of temperature and density using only a single cloud. We observe that the scattering rate is increased below the critical temperature for Bose-Einstein condensation by a factor of 3 compared to the single-atom scattering rate. We show that current atom-light interaction models to second order of the density show a similar increase, where the magnitude of the effect depends on the model that is used to calculate the pair-correlation function. This confirms that the effect of quantum statistics on the index of refraction is dominant in this regime.

Rayleigh surface wave interaction with the 2D exciton Bose-Einstein condensate

We describe the interaction of a Rayleigh surface acoustic wave (SAW) traveling on the semiconductor substrate with the excitonic gas in a double quantum well located on the substrate surface. We study the SAW attenuation and its velocity renormalization due to the coupling to excitons. Both the deformation potential and piezoelectric mechanisms of the SAW-exciton interaction are considered. We focus on the frequency and excitonic density dependences of the SAW absorption coefficient and velocity renormalization at temperatures both above and well below the critical temperature of Bose-Einstein condensation of the excitonic gas. We demonstrate that the SAW attenuation and velocity renormalization are strongly different below and above the critical temperature.

Transport coefficients from the boson Uehling-Uhlenbeck equation

Expressions for the bulk viscosity, shear viscosity, and thermal conductivity of a quantum degenerate Bose gas above the critical temperature for Bose-Einstein condensation are derived using the Uehling-Uhlenbeck kinetic equation. For contact potentials and hard sphere interactions, the eigenvalues (relaxation rates) of the Uehling-Uhlenbeck collision operator have an upper cutoff. This cutoff requires summation over all discrete eigenvalues and eigenvectors of the collision operator when computing transport coefficients. We numerically compute the shear viscosity and thermal conductivity for any boson gas that interacts via a contact potential. We find that the bulk viscosity of the degenerate boson gas remains identically zero, as it is for the classical gas.

Spin Caloritronics in Noncondensed Bose Gases

We consider coupled spin and heat transport in a two-component atomic Bose gas in the noncondensed state. We find that the transport coefficients show a temperature dependence reflecting the bosonic enhancement of scattering and discuss experimental signatures of the spin-heat coupling in spin accumulation, spin separation, and total dissipation. Close to the critical temperature for Bose-Einstein condensation, we find that the spin-heat coupling is strongly reduced, which is also reflected in the spin caloritronics figure of merit that determines the thermodynamic efficiency of spin-heat conversion.

Observation of Local Temporal Correlations in Trapped Quantum Gases

We measure the temporal pair correlation function g(2)(τ) of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed in situ by using a local, time-resolved single-atom sensitive probing technique. Third- and fourth-order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement. We discuss, finally, the role of interactions. Our results promote temporal correlations as new observables to study the dynamical evolution of ultracold quantum gases.

Suppression of Bose-Einstein condensation in one-dimensional scale-free random potentials

A perfect Bose gas can condensate in one dimension in the presence of a random potential due to the presence of Lifshitz tails in the one-particle density of states. Here, we show that scale-free correlations in the random potential suppress the disorder induced Bose-Einstein condensation (BEC). Within a tight-binding approach, we consider free Bosons moving in a scale-free correlated random potential with spectral density decaying as $1/{k}^{\ensuremath{\alpha}}$. The critical temperature for BEC is shown to vanish in chains with a binary nonstationary potential $(\ensuremath{\alpha}>1)$. On the other hand, a weaker suppression of BEC takes place in nonbinarized scale-free potentials. After a slightly increase in the stationary regime, the BEC transition temperature continuously decays as the spectral exponent $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$.

Spin-Drag Hall Effect in a Rotating Bose Mixture

We show that in a rotating two-component Bose mixture, the spin drag between the two different spin species shows a Hall effect. This spin-drag Hall effect can be observed experimentally by studying the out-of-phase dipole mode of the mixture. We determine the damping of this mode due to spin drag as a function of temperature. We find that due to Bose stimulation there is a strong enhancement of the damping for temperatures close to the critical temperature for Bose-Einstein condensation.

Enhanced and Reduced Atom Number Fluctuations in a BEC Splitter

We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to -4.9 dB below the atom shot noise level. Fluctuations rise to more than +3.8 dB close to Tc, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the supershot noise fluctuations directly originate from quantum statistics.

Bose gas in a single-beam optical dipole trap

We study an ultracold Bose gas in an optical dipole trap consisting of one single focused laser beam. An analytical expression for the corresponding density of states beyond the usual harmonic approximation is obtained. We are thus able to discuss the existence of a critical temperature for Bose-Einstein condensation and find that the phase transition must be enabled by a cutoff near the threshold. Moreover, we study the dynamics of evaporative cooling and observe significant deviations from the findings for the well-established harmonic approximation. Furthermore, we investigate Bose-Einstein condensates in such a trap in Thomas-Fermi approximation and determine analytical expressions for chemical potential, internal energy, and Thomas-Fermi radii beyond the usual harmonic approximation.

Critical temperature of dilute Bose gases

We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and it should be exact to lowest order in the scattering length of the particle interactions. We find that the change in the critical temperature is proportional to a rho^{1/3} with constant c = -2.33; this contradicts the current consensus among physicists.

Rigorous upper bound on the critical temperature of dilute Bose gases

We prove exponential decay of the off-diagonal correlation function in the two-dimensional homogeneous Bose gas when a2ρ is small and the temperature T satisfies T>4πρ/ln|ln(a2ρ)|. Here, a is the scattering length of the repulsive interaction potential and ρ is the density. To the leading order in a2ρ, this bound agrees with the expected critical temperature for superfluidity. In the three-dimensional Bose gas, exponential decay is proved when T−Tc(0)/Tc(0)>5√aρ1/3, where Tc(0) is the critical temperature of the ideal gas. While this condition is not expected to be sharp, it gives a rigorous upper bound on the critical temperature for Bose-Einstein condensation.

Strongly interacting Bose gas: Nozières and Schmitt-Rink theory and beyond

We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance, and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozieres and Schmitt-Rink the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold Cs133 atoms where recent measurements indicate that the gas may be sufficiently long-lived to explore the many-body physics around a Feshbach resonance.

Critical temperature of antikaon condensation in nuclear matter

We investigate the critical temperature of Bose-Einstein condensation of ${K}^{\ensuremath{-}}$ mesons in neutron star matter. This is studied within the framework of relativistic field theoretical models at finite temperature where nucleon-nucleon and (anti)kaon-nucleon interactions are mediated by the exchange of mesons. The melting of the antikaon condensate is studied for different values of antikaon optical potential depths. We find that the critical temperature of antikaon condensation increases with baryon number density. Further it is noted that the critical temperature is lowered as antikaon optical potential becomes less attractive. We also construct the phase diagram of neutron star matter with ${K}^{\ensuremath{-}}$ condensate.

Critical temperature for Bose-Einstein condensation in quartic potentials

The quartic confining potential has emerged as a key ingredient to obtain fast rotating vortices in BEC as well as observation of quantum phase transitions in optical lattices. We calculate the critical temperature Tc of bosons at which normal to BEC transition occurs for the quartic confining potential. Further more, we evaluate the effect of finite particle number on Tc and find that ΔTc/Tc is larger in quartic potential as compared to quadratic potential for number of particles <105. Interestingly, the situation is reversed if the number of particles is $\gtrsim$ 105.

Thermodynamics of solitonic matter waves in a toroidal trap

We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.