Realization Of Bose-Einstein Condensation Research Articles

Double dome structure of the Bose–Einstein condensation in diluted S = 3/2 quantum magnets

Bose–Einstein condensation (BEC) in quantum magnets, where bosonic spin excitations condense into ordered ground states, is a realization of BEC in a thermodynamic limit. Although previous magnetic BEC studies have focused on magnets with small spins of S ≤ 1, larger spin systems potentially possess richer physics because of the multiple excitations on a single site level. Here, we show the evolution of the magnetic phase diagram of S = 3/2 quantum magnet Ba2CoGe2O7 when the averaged interaction J is controlled by a dilution of magnetic sites. By partial substitution of Co with nonmagnetic Zn, the magnetic order dome transforms into a double dome structure, which can be explained by three kinds of magnetic BECs with distinct excitations. Furthermore, we show the importance of the randomness effects induced by the quenched disorder: we discuss the relevance of geometrical percolation and Bose/Mott glass physics near the BEC quantum critical point.

Controlling the Nonlinear Relaxation of Quantized Propagating Magnons in Nanodevices.

Relaxation of linear magnetization dynamics is well described by the viscous Gilbert damping processes. However, for strong excitations, nonlinear damping processes such as the decay via magnon-magnon interactions emerge and trigger additional relaxation channels. Here, we use space- and time-resolved microfocused Brillouin light scattering spectroscopy and micromagnetic simulations to investigate the nonlinear relaxation of strongly driven propagating spin waves in yttrium iron garnet nanoconduits. We show that the nonlinear magnon relaxation in this highly quantized system possesses intermodal features, i.e., magnons scatter to higher-order quantized modes through a cascade of scattering events. We further show how to control such intermodal dissipation processes by quantization of the magnon band in single-mode devices, where this phenomenon approaches its fundamental limit. Our study extends the knowledge about nonlinear propagating spin waves in nanostructures which is essential for the construction of advanced spin-wave elements as well as the realization of Bose-Einstein condensates in scaled systems.

How creating one additional well can generate Bose-Einstein condensation

The realization of Bose-Einstein condensation in ultracold trapped gases has led to a revival of interest in this fascinating quantum phenomenon. This experimental achievement necessitated both extremely low temperatures and sufficiently weak interactions. Particularly in reduced spatial dimensionality even an infinitesimal interaction immediately leads to a departure to quasi-condensation. We propose a system of strongly interacting bosons, which overcomes those obstacles by exhibiting a number of intriguing related features: (i) The tuning of just a single control parameter drives a transition from quasi-condensation to complete condensation, (ii) the destructive influence of strong interactions is compensated by the respective increased mobility, (iii) topology plays a crucial role since a crossover from one- to ‘infinite’-dimensionality is simulated, (iv) a ground state gap opens, which makes the condensation robust to thermal noise. Remarkably, all these features can be derived by analytical and exact numerical means despite the non-perturbative character of the system.

Phases and collective modes of bosons in a triangular lattice at finite temperature: A cluster mean field study

Motivated by the realization of Bose-Einstein condensates (BEC) in non-cubic lattices, in this work we study the phases and collective excitation of bosons with nearest neighbor interaction in a triangular lattice at finite temperature, using mean field (MF) and cluster mean field (CMF) theory. We compute the finite temperature phase diagram both for hardcore and softcore bosons, as well analyze the effect of correlation arising due to lattice frustration and interaction systematically using CMF method. A semi-analytic estimate of the transition temperatures between different phases are derived within the framework of MF Landau theory, particularly for hardcore bosons. Apart from the usual phases such as density waves (DW) and superfluid (SF), we also characterize different supersolids (SS). These phases and their transitions at finite temperature are identified from the collective modes. The low lying excitations, particularly Goldstone and Higgs modes of the supersolid can be detected in the ongoing cold atom experiments.

Effects of linear Zeeman splitting on the dynamics of bright solitons in spin-orbit coupled Bose-Einstein condensates

Solitons as self-supported solitary waves are one of the most fundamental objects in nonlinear science. With the realization of Bose-Einstein condensate, matter-wave solitons have aroused enormous interest due to their potential applications in atomic transport and atomic interferometer. In recent years, the artificial spin-orbit coupling has been realized in ultracold atoms, thus providing a new platform to study the nonlinear matter wave solitons under a gauge field, and a variety of novel soliton phenomena have been successively predicted. In this paper, we analyze the effects of linear Zeeman splitting on the dynamics of bright-bright solitons in spin-orbit coupled two-component Bose-Einstein condensate, via the variational approximation and the numerical simulation of Gross-Pitaevskii (GP) equations. For the SU(2) spin-rotational invariant attractive atomic interaction in a uniform case without external trap, we take a hyperbolic secant function as the variational Ansatz for bright soliton in variational approximation, and derive the Euler-Lagrange equations describing the evolution of the Ansatz parameters. By solving the time-independent Euler-Lagrange equations, we find two stationary solitons each with a finite momentum for a weak spin-orbit coupling due to the linear Zeeman splitting. Linearizing the Euler-Lagrange equations around these stationary solitons, we further obtain a zero-energy Goldstone mode and an oscillation mode with frequency related to linear Zeeman splitting: the former indicates that the continuous translational symmetry of the stationary solitons will be broken under a perturbation, and the later shows that the stationary solitons will oscillate under a perturbation. Furthermore, by solving the time-dependent Euler-Lagrange equations, we also obtain the exact full dynamical solutions of Ansatz parameters, and observe that the linear Zeeman splitting affects the period and velocity of soliton's oscillation and linear motion, which may provide a new method to control the dynamics of solitons. All the variational calculations are also confirmed directly by the numerical simulation of GP equations.

Effective-mass approach to controlling double-well dynamics of atomic Bose-Einstein condensates

The realization of Bose-Einstein condensation in dilute atomic gases opens an exciting way to quantum mechanics and begins a new area of quantum simulation. As a macroscopic quantum object and a many-body bosonic system, the Bose-Einstein condensates can show numerous exotic quantum effects and have naturally attracted great attention. One of the simplest quantum many-body systems to be realized experimentally and studied theoretically is ultra-cold atoms in a double-well potential. This system can exhibit a great variety of quantum interference phenomena such as tunneling oscillation, self-trapping and the entanglement of macroscopic superpositions. Specifically, the double-well potentials built by optical or magnetic fields are easy to change and the many-body interaction between ultra-cold atoms can be changed by the method of Feshbach resonance, enabling the precise quantum control of the double-well dynamics of the condensates. In the present work, we study the dynamics of a condensate in a trapping potential consisting of an unalterable double-well trap and an additional moving optical lattice. If the lattice space is much smaller than the size of the double-well trap, the system can be simplified into a double-well trapped condensate with a tunable effective mass. Using the mean-field factorization assumption, together with a two-mode approximation, we obtain the analytic expressions for the dependence of the tunneling rate and the self-collision strength on the effective mass. The tunneling rate decays and the collision strength grows up with the increase of the effective mass. As a consequence of their different changes, we conclude that the adjustment of the effective mass of the ultra-cold atoms, rather than the changing of the trap barrier or adjusting of the atomic scattering length, is an alternative approach to controlling the double-well dynamics of the condensate. Via numerical simulations of the mean-field dynamical equations with some realistic parameters, we show that a transition between the quantum coherent tunneling and the self-trapping behaviors is experimentally realizable with the mass-control approach. Specifically, we show that the approach is still valid for the case of negative mass. Moreover, we find that the negative-mass case can be used even to stimulate the double-well dynamics of the condensate with a negative atomic scattering length.

Buffer-Gas Cooled Bose-Einstein Condensate

We report the creation of a Bose-Einstein condensate using buffer-gas cooling, the first realization of Bose-Einstein condensation using a broadly general method which relies neither on laser cooling nor unique atom-surface properties. Metastable helium ((4)He*) is buffer-gas cooled, magnetically trapped, and evaporatively cooled to quantum degeneracy. 10(11) atoms are initially trapped, leading to Bose-Einstein condensation at a critical temperature of 5 microK and threshold atom number of 1.1 x 10(6). This method is applicable to a wide array of paramagnetic atoms and molecules, many of which are impractical to laser cool and impossible to surface cool.

Alpha Particle Condensation in Nuclear Systems

Quantum condensation of particles is one of the most amazing phenomena exhibited by many-body systems. Familiar yet striking examples known for many decades include superconductivity of metals at low temperatures and superfluidity of liquid 4He. More recently the realization of Bose-Einstein condensation of ultracold atoms in traps has created an exciting new field of quantum many-body physics. Also, atomic nuclei and neutron stars can experience quantum condensation of fermion pairs and display superfluid properties. However, in nuclear physics the most tightly bound light cluster is not a pair but a quartet, namely the alpha particle. Can we then expect α-particle condensation in nuclei? Before pursuing to this question, let us make some general remarks. It is a fact that quartetting is more pronounced in nuclei than in most other Fermi systems. And the dominance of quartetting can be traced to the fact that nucleons can exist in four different internal states: proton and neutron, each with spin up or down, all attracting each other. Therefore, a shell model picture in which the α-particle is the first doubly magic nucleus, with a filled 0S–level, is valid (see below, Fig. 2). Moreover, the α-particle is especially stiff, with its first excited state lying quite high, at ∼ 20 MeV. The search is now on for quartets in systems other than nuclei.

Bose-Einstein condensates with attractive1∕rinteraction: The case of self-trapping

Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive $1∕r$ interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate ``atomic'' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters ${N}^{2}a∕{a}_{u}$ and $\ensuremath{\gamma}∕{N}^{2}$, where $N$ is the particle number, $a$ the scattering length, ${a}_{u}$ the ``Bohr'' radius, and $\ensuremath{\gamma}$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.

Introduction

During the last few years the physics of ultracold atomic gases has experienced an extraordinary development, mostly due to the experimental realization of Bose-Einstein condensation (BEC). This development has being certainly interdisciplinary, bridging the gaps among very different areas, including atomic and molecular physics, quantum optics, condensed matter and solid-state physics, nonlinear physics, quantum information theory, etc.

Creation of ultracold molecules from a Fermi gas of atoms.

Following the realization of Bose-Einstein condensates in atomic gases, an experimental challenge is the production of molecular gases in the quantum regime. A promising approach is to create the molecular gas directly from an ultracold atomic gas; for example, bosonic atoms in a Bose-Einstein condensate have been coupled to electronic ground-state molecules through photoassociation or a magnetic field Feshbach resonance. The availability of atomic Fermi gases offers the prospect of coupling fermionic atoms to bosonic molecules, thus altering the quantum statistics of the system. Such a coupling would be closely related to the pairing mechanism in a fermionic superfluid, predicted to occur near a Feshbach resonance. Here we report the creation and quantitative characterization of ultracold 40K2 molecules. Starting with a quantum degenerate Fermi gas of atoms at a temperature of less than 150 nK, we scan the system over a Feshbach resonance to create adiabatically more than 250,000 trapped molecules; these can be converted back to atoms by reversing the scan. The small binding energy of the molecules is controlled by detuning the magnetic field away from the Feshbach resonance, and can be varied over a wide range. We directly detect these weakly bound molecules through their radio-frequency photodissociation spectra; these probe the molecular wavefunction, and yield binding energies that are consistent with theory.

Realization of Bose-Einstein condensates in lower dimensions.

Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The crossover into two-dimensional and one-dimensional condensates was observed by a change in aspect ratio and by the release energy converging to a nonzero value when the number of trapped atoms was reduced.

TRAPPED BOSE GAS: MEAN-FIELD APPROXIMATION AND BEYOND

The recent realization of Bose-Einstein condensation in atomic gases opens new possibilities for observation of macroscopic quantum phenomena. There are two important features of the system - weak interaction and significant spatial inhomogeneity. Because of this inhomogeneity a non-trivial "zeroth-order" theory exists, compared to the "first-order" Bogolubov theory. This theory is based on the mean-field Gross-Pitaevskii equation for the condensate ψ-function. The equation is classical in its essence but contains the ℏ constant explicitly. Phenomena such as collective modes, interference, tunneling, Josephson-like current and quantized vortex lines can be described using this equation. The study of deviations from the zeroth-order theory arising from zero-point and thermal fluctuations is also of great interest. Thermal fluctuations are described by elementary excitations which define the thermodynamic behaviour of the system and result in Landau-type damping of collective modes. Fluctuations of the phase of the condensate wave function restrict the monochromaticity of the Josephson current. Fluctuations of the numbers of quanta result in the quantum collapse-revival of the collective oscillations. This phenomenon is considered in some details. Collapse time for the JILA experimental conditions turns out to be of the order of seconds.