Bose-Einstein Condensation Experiments Research Articles

Excitation and manipulation of recurring rogue waves via nonlinear compression

We theoretically propose a feasible scheme to generate high-density waves and manipulate them quantitatively. We show that a wave with greater density compression called “recurring rogue wave” can be excited by first generating a rogue wave via quenching and Gaussian space modulation techniques followed by employing a nonlinear compression method. The formation of recurring rogue wave is verified to be a consequence of the combined interaction of nonlinear compression and “self compression”. We find that the maximal density of recurring rogue wave exhibits a nonmonotonic dependence on compression time, which allows us to manipulate recurring rogue waves quantitatively through changing compression time and modulation parameters within a certain range. The analytical results based on variational method qualitatively support the numerical simulation results. Our study provides potential strategies for efficiently generating high-density waves in Bose–Einstein condensate experiments.

The controlled fission, fusion and collision behavior of two species Bose–Einstein condensates with an optical potential

Abstract By using the Crank–Nicolson method, we investigate numerically the dynamical properties of bright–bright solitons in two species Bose–Einstein condensates (BECs) trapped in an optical lattice. We confirm that the soliton splitting behavior occurs at a critical depth of optical potential. The splitting behavior of solitons and the fusion behavior of condensates can be accurately controlled by adjusting the depth and lattice parameter of optical potential, the initial amplitude and position of solitons, and the interspecies interactions. When the lattice parameter is fixed but the interspecies interaction increased exponentially with the time, each soliton splits into two soltions with different amplitude, and partial fusion of two species BECs can be found. While the interspecies interaction remains unchanged but the lattice parameter increases exponentially with the time, interestingly, the bright solitons with zero initial velocity can pass through each other and accomplish a transmission collision. Furthermore, for the case of both the interspecies interaction and lattice parameter increased exponentially with the time, a head-on collision of the bright solitons in two species BECs occurred. After the collision, each soliton splits into two soltions with equal amplitude. Meanwhile, the complete fusion of two species BECs can be observed. The relevant results can provide help for the precise manipulation of BECs experiments.

Static and dynamic properties of self-bound droplets of light in hot vapors

The authors explore analogies between self-bound droplet states in Bose-Einstein condensates (BECs) and the propagation of light in nonlinear hot vapor mediums. They establish a mapping between the experimental parameters used in BEC experiments and those needed to observe the analogous phenomenon in hot atomic vapors.

Equatorial waves in rotating bubble-trapped superfluids

As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation by a Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian is topologically nontrivial. Furthermore, we solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.

Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions.

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range [0,2π], which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an n-valley dark soliton could be in the range [0,nπ], supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.

SU(1, 1) squeezed state

SU(1, 1) coherent and squeezed states have been widely studied in optical, hybrid atom–light, and spinor Bose–Einstein condensate experiments. Traditionally, the definition of SU(1, 1) squeezing refers to the uncertainty relationship, which implies that the SU(1, 1) coherent state is already squeezed if it is placed in an appropriate system of coordinates. In this report we investigate the basic concept of SU(1, 1) squeezing and discuss the principle for the generation of squeezed states. We establish a new definition of the squeezing criterion for the SU(1, 1) states. We study the dynamical properties in an atom–molecule system and show that the SU(1, 1) squeezed state can be generated with a nonlinear atomic interaction, which is similar to the one-axis twisting mechanism in spin squeezing. We also discuss the effect of the atomic number on squeezing, and show that the optimal squeezing and optimal squeezing angle exhibit a sudden transition at a fixed atomic number value.

Nonlocal Pair Correlations in a Higher-Order Bose Gas Soliton.

The truncated Wigner and positive-P phase-space representations are used to study the dynamics of a one-dimensional Bose gas. This allows calculations of the breathing quantum dynamics of higher-order solitons with 10^{3}-10^{5} particles, as in realistic Bose-Einstein condensation experiments. Although classically stable, these decay quantum mechanically. Our calculations show that there are large nonlocal correlations and nonclassical quantum entanglement.

Quantum quenches, sonic horizons, and the Hawking radiation in a class of exactly solvable models

Taking advantage of the known exact mapping of the one-dimensional hard core Bose (HCB) fluid onto a non-interacting spinless fermion gas, we examine in full detail a thought experiment on cold atoms confined in a quasi-one-dimensional trap, in order to investigate the emergence of the analogue Hawking radiation. The dynamics of a gas of interacting bosons impinging on an external potential is exactly tracked up to the reach of a stationary state. Under few strict conditions on the experimental parameters, the stationary state is shown to be described asymptotically by a thermal distribution, precisely at the expected (analogue) Hawking temperature. However, we find that in most experimental conditions the emerging ``Hawking-like radiation'' is not thermal. This analysis provides a novel many-body microscopic interpretation of the Hawking mechanism, together with useful limits and conditions for the design of future experiments in Bose-Einstein condensates.

Antireflection coated semiconductor laser amplifier for Bose-Einstein condensation experiments

We present a slave laser highly suitable for the preparation and detection of 87Rb Bose-Einstein condensates (BEC). A highly anti-reflection coated laser diode serves as an optical amplifier, which requires neither active temperature stabilization nor dedicated equipment monitoring the spectral purity of the amplified light. The laser power can be controlled with a precision of 10 μW in 70 mW with relative fluctuations down to 2 × 10−4. Due to its simplicity and reliability, this slave laser will be a useful tool for laboratory, mobile, or even space-based cold-atom experiments. By the way of demonstration this slave laser was used as the sole 780 nm light-source in the production of 3 × 104 BECs in a hybrid magnetic/dipole trap.

Large-Scale Bose-Einstein Condensation in an Atomic Gas by Applying an Electric Field

Large-scale Bose-Einstein condensation (BEC) of cesium atoms has been observed (T=343K). The technical bottleneck of BEC is very small trapping volume (10-8cm3), which made the number of condensed atoms still stagnant (less than 107), much smaller than normal condensation (more than 1013), large-scale BEC has never been observed. In BEC experiment, scientists have applied magnetic field (used to trap atoms) and laser (used to cool atoms), but never considered applying electric field, because they think that all kinds of atoms are non-polar atoms. The breakthrough of the bottleneck lies in the application of electric field. In theory, despite 6s and 6p states of cesium are not degenerate, but Cs may be polar atom doesn't conflict with quantum mechanics because it is hydrogen-like atom. When an electric field was applied, Cs atoms become dipoles, therefore large-scale BEC can be observed. BEC experiment of cesium has been redone. From the entropy S=0, critical voltage Vc=78V. When V 0; when V > Vc, S Vc, almost all Cs atoms (bosons) are in exactly the same state，according to Feynman, “the quantum physics is the same thing as the classical physics”, so our classical theory can explain BEC experiment satisfactorily. Ultra-low temperature is to make Bose gas phase transition, we used critical voltage to achieve phase transition, ultra-low temperature is no longer necessary. Five innovative formulas were first reported in the history of physics, the publication of this article marking mankind will enter a new era of polar atoms.

High-Power Narrow-Linewidth Tunable 670.8-nm Master Oscillator Power Amplifier With High Efficiency

A highly efficient 670.8-nm high-power narrow-linewidth wavelength-tunable laser source with master oscillator power amplifier structure is demonstrated, which yielded CW output power of 4.5 W with spectral linewidth of 0.3 pm and mode-hop free tuning range of 52 pm (35 GHz). The total conversion efficiency of 20% was achieved. The developed narrow-linewidth tunable laser source can provide better performance than others ever reported at 670.8 nm for many applications, such as laser isotope separation, Bose–Einstein condensation experiments, and mid-infrared laser generation.

Dynamics of dark-bright vector solitons in Bose-Einstein condensates

We analyze the dynamics of two-component vector solitons, namely bright-in-dark solitons, via the variational approximation in Bose-Einstein condensates. The system is described by a vector nonlinear Schr\"odinger equation appropriate to multi-component Bose-Einstein condensates (BECs). The variational approximation is based on hyperbolic secant (hyperbolic tangent) for the bright (dark) component, which leads to a system of coupled ordinary differential equations for the evolution of the ansatz parameters. We obtain the oscillation dynamics of two-component dark-bright vector solitons. Analytical calculations are performed for same-width components in the vector soliton and numerical calculations extend the results to arbitrary widths. We calculate the binding energy of the system and find it proportional to the intercomponent coupling interaction, and numerically demonstrate the break up or unbinding of a dark-bright soliton. Our calculations explore observable eigenmodes, namely the internal oscillation eigenmode and the Goldstone eigenmode. We find analytically that the density of the bright component is required to be less than the density of the dark component in order to find the internal oscillation eigenmode of the vector soliton and support the existence of the dark-bright soliton. This outcome is confirmed by numerical results. Numerically, we find that the oscillation frequency is amplitude independent. For dark-bright vector solitons in $^{87}$Rb we find that the oscillation frequency range is 90 to 405 Hz, and therefore observable in multi-component BEC experiments.

Theoretical and Experimental Proof of Alkali-Metal Atom as Polar Atom

In addition to polar molecules, there is no polar atom in the natural world, which is a deep-rooted traditional concept that has lasted for more than a century. However, our research showed that alkali-metal atoms form an exception. In theory, we proved that alkali atom may be polar atom doesn't conflict with quantum mechanics, which is a great breakthrough in measurement theory of quantum mechanics. Variation of the capacitance with temperature and density offers a means of separating polar and nonpolar atom, but no one has done these experiments so far. If alkali atom is nonpolar atom, its capacitance should be independent of temperature and density, because atomic nucleus located at the center of the electron cloud. Our experiments showed that Na, K, Rb and Cs atoms are polar atoms, because their capacitance is not only related to temperature, but also to density. Unlike alkali atoms, the capacitance of Hg gas is independent of temperature and density, so mercury is nonpolar atom. Therefore atoms can be divided into two categories: polar and nonpolar atom, this discovery will lead to an exciting revolution in Bose- Einstein condensation (BEC) research and condensed matter physics. BEC experiments have been carried out for decades, but the number of condensed atoms is still very small (<107) because scientists has never applied an electric field. Our innovation lies in the application of an electric field, we don't need magnetic field and lasers. When V=390 volts, condensates contained up to 2.51 × 1017 sodium atoms; when V=350 volts, condensates contained up to 1.93 × 1017 cesium atoms, large-scale BEC at T=343 K or 353 K has been observed. Now scientists generally assume that polar molecules may be used as candidate materials for quantum computers. In the future, polar atoms will replace polar molecules as candidate materials for quantum computers, because of its very small moment of inertia.

Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates

We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalised $n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and $\hat{b}$ are the boson operators for each mode). The correlation manifests as interference fringes in $n$-particle detection probabilities and is also measurable via quadrature phase amplitude and spin squeezing measurements. Measurement of $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle$ enables a quantification of the overall $n$-th order quantum coherence, thus providing an avenue for high efficiency verification of a high-fidelity photonic NOON states. The second criterion is based on a quantification of the measurable spin-squeezing parameter $\xi_{N}$. We apply the criteria to theoretical models of NOON states in lossy interferometers and double-well trapped BECs. By analysing existing BEC experiments, we demonstrate generalised atomic "kitten" states and atomic quantum coherence with $n\gtrapprox10$ atoms.

Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO(2) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.

Signature of Critical Point in Momentum Profile of Trapped Ultracold Bose Gases**Supported by the National Natural Science Foundation of China under Grant No 11104322, and the National Key Basic Research and Development Program of China under Grant No 2011CB921503.

We present a new method to identify the critical point for the Bose-Einstein condensation (BEC) of a trapped Bose gas. We calculate the momentum distribution of an interacting Bose gas near the critical temperature, and find that it deviates significantly from the Gaussian profile as the temperature approaches the critical point. More importantly, the standard deviation between the calculated momentum spectrum and the Gaussian profile at the same temperature shows a turning point at the critical point, which can be used to determine the critical temperature. These predictions are also confirmed by our BEC experiment for magnetically trapped 87Rb gases.

Dynamical phase diagram of Gaussian wave packets in optical lattices.

We study the dynamics of self-trapping in Bose-Einstein condensates (BECs) loaded in deep optical lattices with Gaussian initial conditions, when the dynamics is well described by the discrete nonlinear Schrödinger equation (DNLSE). In the literature an approximate dynamical phase diagram based on a variational approach was introduced to distinguish different dynamical regimes: diffusion, self-trapping, and moving breathers. However, we find that the actual DNLSE dynamics shows a completely different diagram than the variational prediction. We calculate numerically a detailed dynamical phase diagram accurately describing the different dynamical regimes. It exhibits a complex structure that can readily be tested in current experiments in BECs in optical lattices and in optical waveguide arrays. Moreover, we derive an explicit theoretical estimate for the transition to self-trapping in excellent agreement with our numerical findings, which may be a valuable guide as well for future studies on a quantum dynamical phase diagram based on the Bose-Hubbard Hamiltonian.

Critical point of a rotating Bose–Einstein condensates in optical lattice

In this paper, we have considered the critical point (critical atoms’ number and the corresponding critical temperature) of rotating condensate bosons trapped in optical lattices. Our system is formed by loading three dimensional harmonically trapped boson atoms into a 1D (axial direction) or 2D (radial direction) optical lattice. The system subjected to rotating with angular velocity Ω around to the axial direction z-axis. We employ the semiclassical approximation to calculate the critical point. Effects of the optical lattice depth, direction (axial or radial) and the rotation rate on the critical point are investigated using the semiclassical approximation. The calculated results showed that the temperature dependence of the critical point is changed in an optical lattice and depends crucially on the rotation rate. The effect of the finite size for one-dimensional optical lattice case, as required by experiment, is discussed. The outcome results furnish useful qualitatively theoretical results for the future Bose–Einstein condensation experiments in such traps.

Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of $30\,\mathrm{\mu G\,cm^{-1}}$ and a sensor volume of $2\times10^{-5}\,\mathrm{mm}^3$. We predict a spin-projection noise limited magnetic energy resolution of order $\hbar$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle inherent to BEC experiments.

A high-flux BEC source for mobile atom interferometers

Quantum sensors based on coherent matter-waves are precise measurement devices whose ultimate accuracy is achieved with Bose–Einstein condensates (BECs) in extended free fall. This is ideally realized in microgravity environments such as drop towers, ballistic rockets and space platforms. However, the transition from lab-based BEC machines to robust and mobile sources with comparable performance is a challenging endeavor. Here we report on the realization of a miniaturized setup, generating a flux of quantum degenerate 87Rb atoms every 1.6 s. Ensembles of atoms can be produced at a 1 Hz rate. This is achieved by loading a cold atomic beam directly into a multi-layer atom chip that is designed for efficient transfer from laser-cooled to magnetically trapped clouds. The attained flux of degenerate atoms is on par with current lab-based BEC experiments while offering significantly higher repetition rates. Additionally, the flux is approaching those of current interferometers employing Raman-type velocity selection of laser-cooled atoms. The compact and robust design allows for mobile operation in a variety of demanding environments and paves the way for transportable high-precision quantum sensors.