Bose-Einstein Condensation Temperature Research Articles

Ubiquitous light real-space pairing from long-range hopping and interactions

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion (U) and both near- and next-nearest neighbor hopping (t and t′) and attraction (V and V′), for cubic and tetragonal lattices. The presence of t′ and V′ promotes light pairs. For tetragonal lattices, t′<0 pairs can be lighter than non-interacting particles, and d-symmetric pairs form. Close packing transition temperatures, T⁎, are estimated for the Bose-Einstein condensation (BEC) of pairs to be kBT⁎∼0.1t‾, where t‾ is the geometric mean of the hoppings on the Cartesian axes. When pairs have d-symmetry, the condensate has d-wave character. Thus, the presence of both t′ and V′ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

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.

Possibility of Exciton Bose-Einstein Condensation in CdSe Nanoplatelets.

The quasi-two-dimensional exciton subsystem in CdSe nanoplatelets is considered. It is theoretically shown that Bose-Einstein condensation (BEC) of excitons is possible at a nonzero temperature in the approximation of an ideal Bose gas and in the presence of an "energy gap" between the ground and the first excited states of the two-dimensional exciton center of inertia of the translational motion. The condensation temperature (Tc) increases with the width of the "gap" between the ground and the first excited levels of size quantization. It is shown that when the screening effect of free electrons and holes on bound excitons is considered, the BEC temperature of the exciton subsystem increases as compared to the case where this effect is absent. The energy spectrum of the exciton condensate in a CdSe nanoplate is calculated within the framework of the weakly nonideal Bose gas approximation, considering the specifics of two-dimensional Born scattering.

On the uniaxial strain (pressure) derivatives of the critical temperature of superconductivity of La[formula omitted]Sr[formula omitted]CuO4

The uniaxial strain (and pressure) derivatives of the critical temperature of superconductivity (Tc) of La2−xSrxCuO4 (LSCO) cuprate is studied within the extended Holstein–Hubbard model and bipolaronic mechanism of high-Tc superconductivity. The Tc of LSCO cuprate is associated with the Bose–Einstein condensation temperature, TBEC, of an ideal gas of the intersite bipolarons. Working on a modified chain model lattice of cuprates we expressed TBEC as a function of LSCO’s parameters (apical oxygen ion’s mass and its vibration frequency, the periods and the strains of the lattice). Using the experimental values of LSCO parameters the uniaxial strain derivatives and the uniaxial pressure derivatives of Tc i.e. ∂TBEC/∂ɛi and ∂TBEC/∂pi (i=a,c) of LSCO cuprate are calculated as a function of doping level x. The obtained results are compared with the available experimental data. Qualitative and quantitative similarities as well as differences in the doping dependencies of between our ∂TBEC/∂ɛi (∂TBEC/∂pi) and the experimental ∂Tc/∂ɛi (∂Tc/∂pi) (i=a,c) are discussed. Upon carried analysis we concluded that the uniaxial strain (pressure) derivatives of Tc of LSCO cuprate can be interpreted within the bipolaronic mechanism of superconductivity.

Thermodynamic Correlation of the Entropy of Bose–Einstein Condensation Transition to the Lambda Points of Superfluids

Abstract In this work, the authors show an apparent connection in the behaviors of superfluid Helium in its two stable isotopes, where the lambda transition to superfluidity is seen to correspond to a theoretical Bose–Einstein condensation temperature of the ideal parts of the two isotopes. A statistical model for the physical and thermodynamic behaviors is developed based on their known properties, where the equations of the partition function, entropy, and specific heat are constructed in such a way where one term applies to the ideal part of the fluid and the second to its interacting part. The calculated temperatures for the formation of a theoretical Bose–Einstein condensation in the ideal parts of both isotopes almost completely matches their lambda transition temperatures. The models of the two isotopes are very different due to the fermionic nature of Helium-3, for which the model is formed based on the Bardeen–Cooper–Schrieffer (BCS) theory of Cooper pairs of fermions. Using this formulation, the Bose–Einstein condensation temperature for the pairs of Helium-3 atoms is calculated, as opposed to the condensation temperature for Helium-4, which is directly derived from the bosonic atoms, leading to its much lower value than Helium-4.

Strong coupling of single plasmonic nanoparticles and nanogaps with quantum emitters

In cavity quantum electrodynamics, when the interaction between quantum emitter and cavity mode is strong enough to overcome the mean decay rate of the system, it will enter into a strong coupling regime, thereby forming part-light part-matter polariton states. Strong coupling can serve as a promising platform for room temperature Bose-Einstein condensation, polariton lasing, single photon nonlinearity, quantum information, etc. Localized surface plasmons supported by single metal nanostructures possess extremely small mode volume, which is favorable for realizing strong coupling. Moreover, the nanoscale dimensions of plasmonic structures can facilitate the miniaturization of strong coupling systems. Here, the research progress of strong plasmon-exciton coupling between single metal nanoparticles/nanogaps and quantum emitters is reviewed. The theory background of strong coupling is first introduced, including quantum treatment, classical coupled oscillator model, as well as the analytical expressions for scattering and photoluminescence spectra. Then, strong coupling between different kinds of plasmonic nanostructures and quantum emitters is reviewed. Single metal nanoparticles, nanoparticle dimers, and nanoparticle-on-mirror structures constitute the most typical plasmonic nanostructures. The nanogaps in the latter two systems can highly concentrate electromagnetic field, providing optical nanocavities with smaller mode volume than single nanoparticles. Therefore, the larger coupling strength can be achieved in the nanogap systems, which is conducive to strong coupling at the single-exciton level. In addition, the active tuning of strong coupling based separately on thermal, electrical and optical means are reviewed. The energy and oscillator strength of the excitons in transition metal dichalcogenide (TMDC) monolayers are dependent on temperature. Therefore, the strong coupling can be tuned by heating or cooling the system. The excitons in TMDC monolayers can also be tuned by electrical gating, enabling electrical control of strong coupling. Optically tuning the quantum emitters provides another way to actively control the strong coupling. Overall, the research on active tuning of strong plasmon-exciton coupling is still very limited, and more investigations are needed. Finally, this review is concluded with a short summary and the prospect of this field.

Organic-2D Material Heterostructures: A Promising Platform for Exciton Condensation and Multiplication.

We predict that high temperature Bose-Einstein condensation of charge transfer excitons can be achieved in organic-two-dimensional (2D) material heterostructures, at ∼50-100 K. Unlike 2D bilayers that can be angle-misaligned, organic-2D systems generally have momentum-direct low-energy excitons, thus favoring condensation. Our predictions are obtained for ZnPc-MoS2 using state-of-the-art first-principles calculations with the GW-BSE approach. The exciton energies we predict are in excellent agreement with recent experiments. The lowest energy charge transfer excitons in ZnPc-MoS2 are strongly bound with a spatial extent of ∼1-2 nm and long lifetimes (τ0 ∼ 1 ns), making them ideal for exciton condensation. We also predict the emergence of inter-ZnPc excitons that are stabilized by the interaction of the molecules with the 2D substrate. This novel way of stabilizing intermolecular excitons by indirect substrate mediation suggests design strategies for singlet fission and exciton multiplication, which are important to overcome the Shockley-Queisser efficiency limit in solar cells.

Electromagnetic quantum shifts in relativistic Bose-Einstein condensation

We compute deviations from ideal gas behavior of the pressure, density, and Bose-Einstein condensation temperature of a relativistic gas of charged scalar bosons caused by the current-current interaction induced by electromagnetic quantum fluctuations treated via scalar quantum electrodynamics. We obtain expressions for those quantities in the ultra-relativistic and nonrelativistic limits, and present numerical results for the relativistic case.

Continued Roots, Power Transform and Critical Properties

We consider the problem of calculation of the critical amplitudes at infinity by means of the self-similar continued root approximants. Region of applicability of the continued root approximants is extended from the determinate (convergent) problem with well-defined conditions studied before by Gluzman and Yukalov (Phys. Lett. A 377 2012, 124), to the indeterminate (divergent) problem my means of power transformation. Most challenging indeterminate for the continued roots problems of calculating critical amplitudes, can be successfully attacked by performing proper power transformation to be found from the optimization imposed on the parameters of power transform. The self-similar continued roots were derived by systematically applying the algebraic self-similar renormalization to each and every level of interactions with their strength increasing, while the algebraic renormalization follows from the fundamental symmetry principle of functional self-similarity, realized constructively in the space of approximations. Our approach to the solution of the indeterminate problem is to replace it with the determinate problem, but with some unknown control parameter b in place of the known critical index β. From optimization conditions b is found in the way making the problem determinate and convergent. The index β is hidden under the carpet and replaced by b. The idea is applied to various, mostly quantum-mechanical problems. In particular, the method allows us to solve the problem of Bose-Einstein condensation temperature with good accuracy.

Thermodynamic stability, compressibility matrices, and effects of mediated interactions in a strongly interacting Bose-Fermi mixture

We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $-U_{\rm BF}<0$ associated with a hetero-nuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction $U_{\rm BB}\ge 0$. Including strong hetero-pairing fluctuations associated with the former interaction within the self-consistent $T$-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regime with respect $-U_{\rm BF}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature $T_{\rm clp}$ (leading to density collapse). When $U_{\rm BB}=0$, $T_{\rm clp}$ is always higher than the Bose-Einstein condensation (BEC) temperature $T_{\rm c}$. When $U_{\rm BB}>0$, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the hetero-pairing interaction $-U_{\rm BF}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to inter-particle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.

Many-body effects and quantum fluctuations for discrete time crystals in Bose–Einstein condensates

We present a fully comprehensive multi-mode quantum treatment based on the truncated Wigner approximation (TWA) to study many-body effects and effects of quantum fluctuations on the formation of a discrete time crystal (DTC) in a Bose–Einstein condensate (BEC) bouncing resonantly on a periodically driven atom mirror. Zero-range contact interactions between the bosonic atoms are assumed. Our theoretical approach avoids the restrictions both of mean-field theory, where all bosons are assumed to remain in a single mode, and of time-dependent Bogoliubov theory, which assumes boson depletion from the condensate mode is small. We show that the mean-field and time-dependent Bogoliubov approaches can be derived as approximations to the TWA treatment. Differing initial conditions, such as a finite temperature BEC, can also be treated. For realistic initial conditions corresponding to a harmonic trap condensate mode function, our TWA calculations performed for period-doubling agree broadly with recent mean-field calculations for times out to at least 2000 mirror oscillations, except at interaction strengths very close to the threshold value for DTC formation where the position probability density differs significantly from that determined from mean-field theory. For typical attractive interaction strengths above the threshold value for DTC formation and for the chosen trap and driving parameters, the TWA calculations indicate a quantum depletion due to quantum many-body fluctuations of less than about two atoms out of a total of 600 atoms at times corresponding to 2000 mirror oscillations, in agreement with time-dependent Bogoliubov theory calculations. On the other hand, for interaction strengths very close to the threshold value for DTC formation, the TWA calculations predict a large quantum depletion—as high as about 260 atoms out of 600. We also show that the mean energy per particle of the DTC does not increase significantly for times out to at least 2000 mirror oscillations and typically oscillates around an average value close to its initial value; so TWA theory predicts the absence of thermalisation. Finally, we find that the dynamical behaviour of our system is largely independent of whether the boson–boson interaction is attractive or repulsive, and that it is possible to create a stable DTC based on repulsive interactions.

Goldstino spectrum in an ultracold Bose-Fermi mixture with explicitly broken supersymmetry

We theoretically investigate a supersymmetric collective mode called Goldstino in a Bose-Fermi mixture. The explicit supersymmetry breaking, which is unavoidable in cold atom experiments, is considered. We derive the Gell-Mann--Oakes-Renner (GOR) relation for the Goldstino, which gives the relation between the energy gap at the zero momentum and the explicit breaking term. We also numerically evaluate the gap of Goldstino above the Bose-Einstein condensation temperature within the random phase approximation (RPA). While the gap obtained from the GOR relation coincides with that in the RPA for the mass-balanced system, there is a deviation from the GOR relation in the mass-imbalanced system. We point out the deviation becomes large when the Goldstino pole is close to the branch point, although it is parametrically a higher order with respect to the mass-imbalanced parameter. To examine the existence of the goldstino pole in realistic cold atomic systems, we show how the mass-imbalance effect appears in $^6$Li-$^7$Li, $^{40}$K-$^{41}$K, and $^{173}$Yb-$^{174}$Yb mixtures. Furthermore, we analyze the Goldstino spectral weight in a $^{173}$Yb-$^{174}$Yb mixture with realistic interactions and show a clear peak due to the Goldstino pole. As a possibility to observe the Goldstino spectrum in cold atom experiments, we discuss the effects of the Goldstino pole on the fermionic single-particle excitation as well as the relationship between the GOR relation and Tan's contact.

Microwave coherent spectroscopy of ultracold thulium atoms

Recently, the thulium atom was cooled down to the Bose-Einstein condensation temperature, thus opening a pathway to quantum simulation with this atom. However, successful simulations require instruments to control and readout states of the atom as well as the ability to control the interaction between either different species or different states of the same type of species. In this paper, we provide an experimental demonstration of high-fidelity (over 93%) manipulation of the ground state magnetic sublevels of thulium, which utilizes a simple and efficient design of a microwave (MW) antenna. The coherence time and dephasing rate of the energetically highest hyperfine level of the ground state were also examined.

Thermal destabilization of self-bound ultradilute quantum droplets

We theoretically investigate the temperature effect in a Bose–Bose mixture with attractive inter-species interactions, in the regime where a self-bound ultradilute quantum droplet forms due to the subtle balance between the attractive mean-field force and the repulsive force provided by Lee–Huang–Yang quantum fluctuations. We find that in contrast to quantum fluctuations, thermal fluctuations destabilize the droplet state and completely destroy it above a threshold temperature. We show that the threshold temperature is determined by the intra-species interaction energy. For a three-dimensional Bose–Bose mixture, the threshold temperature is less than one-tenth of the Bose–Einstein condensation temperature under the typical experimental conditions. With increasing temperature, the droplet’s equilibrium density gradually decreases and can be reduced by several tens of percent upon reaching the threshold temperature. We also consider a one-dimensional quantum droplet and find a similar destabilization effect due to thermal fluctuations. The threshold temperature in one dimension is roughly set by the binding energy of the inter-species dimer. The pronounced thermal instability of a self-bound quantum droplet predicted in our work could be examined in future experiments, by measuring the temperature dependence of its central density and observing its sudden disappearance at the threshold temperature.

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.

Bosonic superfluid transport in a quantum point contact

We present a microscopic theory of heat and particle transport of an interacting, low temperature Bose-Einstein condensate in a quantum point contact. We show that, in contrast to charged, fermionic superconductors, bosonic systems feature tunneling processes of condensate elements, leading to the presence of odd-order harmonics in the AC Josephson current. A crucial role is played by an anomalous tunneling process where condensate elements are coherently converted into phonon excitations, leading to even-order harmonics in the AC currents as well as a DC contribution. At low bias, we find dissipative components obeying Ohm's law, and bias-independent nondissipative components, in sharp contrast to fermionic superconductors. Analyzing the DC contribution, we find zero thermopower and Lorenz number at zero temperature, a breakdown of the bosonic Wiedemann-Franz law. These results highlight importance of the anomalous tunneling process inherent to charge neutral superfluids. The consequences could readily be observed in existing cold-atom transport setups.

Translational-Invariant Bipolarons and Superconductivity

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

Трансляционно-инвариантные биполяроны и сверхпроводимость

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Frohlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

Particle Fluctuations in Mesoscopic Bose Systems

Particle fluctuations in mesoscopic Bose systems of arbitrary spatial dimensionality are considered. Both ideal Bose gases and interacting Bose systems are studied in the regions above the Bose–Einstein condensation temperature T c , as well as below this temperature. The strength of particle fluctuations defines whether the system is stable or not. Stability conditions depend on the spatial dimensionality d and on the confining dimension D of the system. The consideration shows that mesoscopic systems, experiencing Bose–Einstein condensation, are stable when: (i) ideal Bose gas is confined in a rectangular box of spatial dimension d &gt; 2 above T c and in a box of d &gt; 4 below T c ; (ii) ideal Bose gas is confined in a power-law trap of a confining dimension D &gt; 2 above T c and of a confining dimension D &gt; 4 below T c ; (iii) the interacting Bose system is confined in a rectangular box of dimension d &gt; 2 above T c , while below T c , particle interactions stabilize the Bose-condensed system, making it stable for d = 3 ; (iv) nonlocal interactions diminish the condensation temperature, as compared with the fluctuations in a system with contact interactions.

Polariton lasing in InGaN quantum wells at room temperature

In this paper, we report the exciton polaritons in both positive and negative detuning micro cavities based on InGaN multi-quantum wells (MQWs) and the first polariton lasing in InGaN/GaN MQWs at room temperature by utilizing a 4.5λ Fabry-Perot (F-P) cavity with double dielectric distributed Bragg reflectors (DBRs). Double thresholds corresponding respectively to polariton lasing and photonic lasing are observed along with half-width narrowing and peak blue-shifts. The threshold of polariton lasing is about half of the threshold of photonic lasing. Our results paved a substantial way for ultra-low threshold lasers and room temperature Bose-Einstein Condensate (BEC) in nitride semiconductors.