Bose-Einstein condensation in BaCuSi 2 O 6

Physical Review B, 2007

We analyze the spin relaxation time 1/T1 for a system made of weakly coupled one dimensional ladders. This system allows to probe the dimensional crossover between a Luttinger liquid and a Bose-Einstein condensate of magnons. We obtain the temperature dependence of 1/T1 in the various dimensional regimes, and discuss the experimental consequences.

Journal of Magnetism and Magnetic Materials, 2007

Torque magnetisation data are presented which probe the line of second order phase transitions approaching the Bose-Einstein condensation (BEC) quantum critical point (QCP) in BaCuSi 2 O 6 . Results reveal that as the temperature is lowered, the phase transition is increasingly dominated by quantum rather than thermal fluctuations near the QCP. r

Physical Review Letters, 2014

Han purple (BaCuSi 2 O 6 ) is not only an ancient pigment, but also a valuable model material for studying Bose-Einstein condensation of magnons in high magnetic fields. Using precise low-temperature structural data and extensive density-functional calculations, we elucidate magnetic couplings in this compound. The resulting magnetic model comprises two types of nonequivalent spin dimers, in excellent agreement with the 63;65 Cu nuclear magnetic resonance data. We further argue that leading interdimer couplings connect the upper site of one dimer to the bottom site of the contiguous dimer, and not the upper-to-upper and bottomto-bottom sites, as assumed previously. This finding is verified by inelastic neutron scattering data and implies the lack of frustration between the layers of spin dimers in BaCuSi 2 O 6 , thus challenging existing theories of the two-dimensional-like Bose-Einstein condensation of magnons in this compound.

Physical Review A, 2002

We develop a simple analytical model based on a variational method to explain the properties of trapped cylindrically symmetric Bose-Einstein condensates (BEC) of varying degrees of anisotropy well into regimes of effective one dimension (1D) and effective two dimension (2D). Our results are accurate in regimes where the Thomas-Fermi approximation breaks down and they are shown to be in agreement with recent experimental data.

JETP Letters, 2015

We discuss a possible origin of the experimentally observed nonlinear contribution to the shift ∆Tc = Tc − T 0 c of the critical temperature Tc in an atomic Bose-Einstein condensate (BEC) with respect to the critical temperature T 0 c of an ideal gas. We found that accounting for a nonlinear (quadratic) Zeeman effect (with applied magnetic field closely matching a Feshbach resonance field B0) in the mean-field approximation results in a rather significant renormalization of the field-free nonlinear contribution b2, namely ∆Tc/T 0 c ≃ b * 2 (a/λT ) 2 (where a is the s-wave scattering length, λT is the thermal wavelength at T 0 c ) with b * 2 = γ 2 b2 and γ = γ(B0). In particular, we predict b * 2 ≃ 42.3 for the B0 ≃ 403G resonance observed in the 39 K BEC. PACS: 67.85.Hj, 67.85.Jk Studies of Bose-Einstein condensates (BECs) continue to be an important subject in modern physics (see, e.g., Refs.[1, 2, 3, 4] and further references therein). Atomic BECs are produced in the laboratory in lasercooled, magnetically-trapped ultra-cold bosonic clouds of different atomic species (including 87 Rb [5, 9], 7 Li [6], 23 N a [7], 1 H [8], 4 He [10], 41 K [11], 133 Cs [12], 174 Y b [13] and 52 Cr [14], among others). Also, a discussion of a relativistic BEC has appeared in Ref.[15] and BECs of photons are most recently under investigation [16]. In addition, BECs are successfully utilized in cosmology and astrophysics [17] as they have been shown to constrain quantum gravity models [18].

Physical Review B, 2008

At zero temperature and strong applied magnetic fields the ground sate of an anisotropic antiferromagnet is a saturated paramagnet with fully aligned spins. We study the quantum phase transition as the field is reduced below an upper critical Hc2 and the system enters a XY-antiferromagnetic phase. Using a bond operator representation we consider a model spin-1 Heisenberg antiferromagnetic with single-ion anisotropy in hyper-cubic lattices under strong magnetic fields. We show that the transition at Hc2 can be interpreted as a Bose-Einstein condensation (BEC) of magnons. The theoretical results are used to analyze our magnetization versus field data in the organic compound N iCl2-4SC(N H2)2 (DTN) at very low temperatures. This is the ideal BEC system to study this transition since Hc2 is sufficiently low to be reached with static magnetic fields (as opposed to pulsed fields). The scaling of the magnetization as a function of field and temperature close to Hc2 shows excellent agreement with the theoretical predictions. It allows to obtain the quantum critical exponents and confirm the BEC nature of the transition at Hc2.

Physical Review A

Quantum-size oscillations of the basic physical characteristics of a confined fermionic condensate are a well-known phenomenon. Its conventional understanding is based on the single-particle physics, whereby the oscillations follow the size-dependent changes in the single-particle density of states. Here we present a study of a cigar-shaped ultracold superfluid Fermi gas, which demonstrates an important many-body aspect of the quantum-size effects, overlooked previously. The many-body physics is revealed in the atypical crossover from the Bardeen-Cooper-Schrieffer (BCS) superfluid to the Bose-Einstein condensate (BEC) induced by the size quantization of the particle motion. Quantized perpendicular spectrum results in the formation of single-particle subbands (shells) so that the aggregate fermionic condensate becomes a coherent mixture of subband condensates. Each time when the lower edge of a subband crosses the chemical potential, the BCS-BEC crossover is approached in this subban...

Physical Review A, 2014

We explore the time evolution of two component Bose-Einstein condensates (BEC's), quasi-1D with respect to their spinor dynamics, following a quench from one component BEC's with a U(1) order parameter into two component condensates with a U(1)×Z2 order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single component attractive BEC.

Physical Review A, 2000

We show that there are three possible phases for a spin-2 spinor Bose condensate, one more compared to the spin-1 case. The order parameters of these phases are the spontaneous magnetization and the singlet pair amplitude. Current estimates of scattering lengths show that all three phases have realizations in optically trapped alkali atoms. There is also a one-to-one correspondence between the structure of a spin-2 spinor Bose condensate and that of a d-wave BCS superfluid.

Tc, 2010

We report exact numerical calculation of chemical potential, condensate fraction and specific heat of N non-interacting bosons confined in an isotropic harmonic oscillator trap in one, two and three dimensions, as also for interacting bosons in a 3D trap. Quasi phase transitions are observed in all these cases, including one-dimension, as shown by a rapid change of all the thermodynamic quantities at the transition point. The change becomes more rapid as N increases in 2D and 3D cases. However with increase in N , the sudden change in the nature of specific heat, gets gradually wiped out in 1D, while it becomes more drastic in 2D and 3D. The sudden change in the nature of condensate fraction and chemical potential as N increases becomes more drastic even in 1D. Defining transition exponents, which characterize the nature of a thermodynamic quantity at the transition point of a quasi phase transition, we evaluate them by careful numerical calculation very near the transition temperature. These exponents are found to be independent of the size of the system and whether the bosons are interacting or not, demonstrating their universality property.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2004

By using a renormalization group analysis, we study the effect of interparticle interactions on the critical temperature T BKT at which the Berezinskii-Kosterlitz-Thouless (BKT) transition occurs for Bose-Einstein condensates loaded at finite temperature in a 2D optical lattice. We find that T BKT decreases as the interaction energy decreases; when U/J = 36/π one has T BKT = 0, signaling the possibility of a quantum phase transition of BKT type.

The European Physical Journal D, 2008

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 ∆Tc/Tc is larger in quartic potential as compared to quadratic potential for number of particles < 10 5 . Interestingly, the situation is reversed if the number of particles is 10 5 .

Mesoscopic interacting Bose-Einstein condensates confined in a few traps display phase transitions that cannot be explained with a mean field theory. By describing each trap as an effective site of a Bose-Hubbard model and using the Schwinger representation of spin operators, these systems can be mapped to spin models. We show that it is possible to define correlations between bosons in such a way that critical behavior is associated to the divergence of a correlation length accompanied by a gapless spectrum in the thermodynamic limit. The latter is now defined as the limit in which the mean field analysis becomes valid. Such description provides critical exponents to the associated phase transitions and encompasses the notion of universality demonstrating thus the potential use of mesoscopic Bose-Einstein condensates as quantum simulators of condensed matter systems.

Journal of Physics B: Atomic, Molecular and Optical Physics, 2000

We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation, and check these results against numerical simulations of the coupled Gross-Pitaevskii equations (GPEs). We find that they can be divided into two general categories. The first class contains solutions with a region of overlap between the components. The other class consists of non-overlapping wavefunctions, and contains also solutions that do not possess the symmetry of the trap. The chemical potential and average energy can be found for both classes within the TF approximation by solving a set of coupled algebraic equations representing the normalization conditions for each component. A ground state minimizing the energy (within both classes of the states) is found for a given set of parameters characterizing the scattering length and confining potential. In the TF approximation, the ground state always shares the symmetry of the trap. However, a full numerical solution of the coupled GPEs, incorporating the kinetic energy of the BEC atoms, can sometimes select a broken-symmetry state as the ground state of the system. We also investigate effects of finite-range interactions on the structure of the ground state.