Kenichi Kasamatsu, Hiromitsu Takeuchi, Muneto Nitta, Makoto Tsubota
We demonstrate theoretically that analogues of D-branes in string theory can be realized in rotating, phase-separated, two-component Bose-Einstein condensates and that they are observable using current experimental techniques. This study raises the possibility of simulating D-branes in the laboratory.
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In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as D-brane solitons. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. Based on the formulation of gauge theory, we introduce the "boojum charge" to characterize the "D-brane soliton" in Bose-Einstein condensates.
We theoretically study the vortex formation from the collision of the domain walls in phase-separated two-component Bose-Einstein condensates. The collision process mimics the tachyon condensation for the annihilation of D-brane and anti-D-brane in string theory. A pair annihilation leaves the quantized vortices with superflow along their core, namely `superflowing cosmic strings'. It is revealed that the line density and the core size of the vortices depend on the initial distance between the walls.
In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane-anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called `tachyon condensation', where the existence of tachyons is attributable to the instability of the brane-anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose-Einstein condensates. We consider annihi…
We study dynamical processes in coherently coupled atomic Bose-Einstein condensates. Josephson effects in ring-shaped and dumbbell geometries are theoretically investigated. Conditions for observation of the Josephson effect are revealed. We found that multicharged persistent current in toroidal condensate can be robust even for supersonic atomic flow. In numerical simulations the acoustic analogues of event horizon in quantized superflow was observed. These theoretical finding open perspectives for investigation of Bose Josephson junctions and quantum aspects of acoustic analogue of Hawking r…
Inspired by a recent experiment by Steinhauer and co-workers, we present a simple model which describes the formation of an acoustic black hole in a Bose-Einstein condensate, allowing an analytical computation of the evolution in time of the corresponding density-density correlator. We show the emergence of analog Hawking radiation out of a "quantum atmosphere" region significantly displaced from the horizon. This is quantitatively studied both at $T=0$ and even in the presence of an initial temperature T, as is always the case experimentally.
We propose a mechanism to create a vorton or three-dimensional skyrmion in phase-separated two-component BECs with the order parameters Psi_1 and Psi_2 of the two condensates. We consider a pair of a domain wall (brane) and an anti-domain wall (anti-brane) stretched by vortices (strings), where the Psi_2 component with a vortex winding is sandwiched by two domains of the Psi_1 component. The vortons appear when the domain wall pair annihilates. Experimentally, this can be realized by preparing the phase separation in the order Psi_1, Psi_2 and Psi_1 components, where the nodal plane of a dark …
We study the quantum fluctuations in a one dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.
Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, grey-soliton-like solutions representing analogues of superconducting Josephson fluxons as well as coupled dark solitons are discussed. Theoretical approximations based on variational formulations are derived. It is found that the presence of a magnetic trap can destabilize the fluxon analogues. However, stabilization is possible by controlling the effective linear coupling between th…
Analogue gravity is based on the simple observation that perturbations propagating in several physical systems can be described by a quantum field theory in a curved spacetime. While phenomena like Hawking radiation are hardly detectable in astrophysical black holes, these effects may be experimentally tested in analogue systems. In this Thesis, focusing on Bose-Einstein condensates, we present our recent results about analogue models of gravity from three main perspectives: as laboratory tests of quantum field theory in curved spacetime, for the techniques that they provide to address various…
We have created an analogue of a black hole in a Bose-Einstein condensate. In this sonic black hole, sound waves, rather than light waves, cannot escape the event horizon. A step-like potential accelerates the flow of the condensate to velocities which cross and exceed the speed of sound by an order of magnitude. The Landau critical velocity is therefore surpassed. The point where the flow velocity equals the speed of sound is the sonic event horizon. The effective gravity is determined from the profiles of the velocity and speed of sound. A simulation finds negative energy excitations, by mea…
Analogue gravity with Bose-Einstein condensates
本文以玻色-爱因斯坦凝聚体为平台，通过理论描述和数值方法，系统介绍了类比黑洞、超辐射和霍金辐射等类比引力现象。
We theoretically propose a finite-size quasi-one-dimensional Bose-Einstein condensate with coherent source and drain placed at its two ends, which can in principle sustain a stationary sonic black hole with a single event horizon. Our analysis is focused on the condensate persistence against quantum fluctuations. We show that similar to white hole-black hole pairs, dynamical instabilities occur. Investigating in detail the instabilities' dependence on the system parameters, we also identify windows of formally infinite black hole lifetimes. By using quantum depletion of the condensate as a dia…
We propose a possible experimental realization of a quantum analogue of Newton's cradle using a configuration which starts from a Bose-Einstein condensate. The system consists of atoms with two internal states trapped in a one dimensional tube with a longitudinal optical lattice and maintained in a strong Tonks-Girardeau regime at maximal filling. In each site the wave function is a superposition of the two atomic states and a disturbance of the wave function propagates along the chain in analogy with the propagation of momentum in the classical Newton's cradle. The quantum travelling signal i…
We study the properties of a $2+1$ dimensional Sonic black hole (SBH) that can be realised, in a quasi-two-dimensional two-component spin-orbit coupled Bose-Einstein condensate (BEC). The corresponding equation for phase fluctuations in the total density mode that describes phonon field in the hydrodynamic approximation is described by a scalar field equation in $2+1$ dimension whose space-time metric is significantly different from that of the SBH realised from a single component BEC that was studied experimentally, and, theoretically meticulously in literature. Given the breakdown of the irr…
Using the coherent state functional integral expression of the partition function, we show that the sine-Gordon model on an analogue curved spacetime arises as the effective quantum field theory for phase fluctuations of a weakly imperfect Bose gas on an incompressible background superfluid flow when these fluctuations are restricted to a subspace of the single-particle Hilbert space. We consider bipartitions of the single-particle Hilbert space relevant to experiments on ultracold bosonic atomic or molecular gases, including, e.g., restriction to high- or low-energy sectors of the dynamics an…
We investigate quantum entanglement in an analogue black hole realized in the flow of a Bose-Einstein condensate. The system is described by a three-mode Gaussian state and we construct the corresponding covariance matrix at zero and finite temperature. We study associated bipartite and tripartite entanglement measures and discuss their experimental observation. We identify a simple optical setup equivalent to the analogue Bose-Einstein black hole which suggests a new way of determining the Hawking temperature and grey-body factor of the system.
We propose emulation of Hawking radiation (HR) by means of acoustic excitations propagating on top of persistent current in an atomic Bose-Einstein condensate (BEC) loaded in an annular confining potential. The setting is initially created as a spatially uniform one, and then switches into a nonuniform configuration, while maintaining uniform BEC density. The eventual setting admits the realization of sonic black and white event horizons with different slopes of the local sound speed. A smooth slope near the white-hole horizon suppresses instabilities in the supersonic region. It is found that…
Many-body gravitating quantum systems with Bose-Einstein condensates and dipolar analogue
利用双模玻色-爱因斯坦凝聚体网络模拟许多体引力量子系统，通过长程耦合实现引力诱导纠缠和退相干的可编程类比平台。
The recent detections of gravitational waves (GWs) by the LIGO and Virgo collaborations have opened the field of GW astronomy, intensifying interest in GWs and other possible detectors sensitive in different frequency ranges. Although strong GW producing events are rare and currently unpredictable, GWs can in principle be simulated in analogue systems at will in the lab. Simulation of GWs in a manifestly quantum system would allow for the study of the interaction of quantum phenomena with GWs. Such predicted interaction is exploited in a recently proposed Bose-Einstein condensate (BEC) based G…
In this paper we propose to apply the analogy between gravity and condensed matter physics to relativistic Bose-Einstein condensates (RBECs), i.e. condensates composed by relativistic constituents. While such systems are not yet a subject of experimental realization, they do provide us with a very rich analogue model of gravity, characterized by several novel features with respect to their non-relativistic counterpart. Relativistic condensates exhibit two (rather than one) quasi-particle excitations, a massless and a massive one, the latter disappearing in the non-relativistic limit. We show t…
Quantum nonlinear effects in the number-conserving analogue gravity of Bose-Einstein condensates
本文研究了绝对零度下玻色-爱因斯坦凝聚体的量子动力学，提出超越 Unruh 线性化范式的非线性类比引力模型，通过引入量子涨落重整化时空度规、矢量场和质量项来考虑准粒子反作用，并应用于宇宙学度规。
We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of $SU$(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions …
The sonic analogue of Hawking radiation can now be experimentally recreated in Bose-Einstein Condensates that contain an acoustic black hole. In these experiments the signal strength and analogue Hawking temperature increase for denser condensates, which however also suffer increased atom losses from inelastic collisions. To determine how these affect analogue Hawking radiation, we numerically simulate creation of the latter in a Bose-Einstein Condensate in the presence of atomic losses. In particular we explore modifications of density-density correlations through which the radiation has been…
The Unruh effect predicts a thermal response for an accelerated detector moving through the vacuum. Here we propose an interferometric scheme to observe an analogue of the circular Unruh effect using a localized laser coupled to a Bose-Einstein condensate (BEC). Quantum fluctuations in the condensate are governed by an effective relativistic field theory, and as demonstrated, the coupled laser field acts as an effective Unruh-DeWitt detector thereof. The effective speed of light is lowered by 12 orders of magnitude to the sound velocity in the BEC. For detectors traveling close to the sound sp…
Collective modes propagating in a moving superfluid are known to satisfy wave equations in a curved space time, with a metric determined by the underlying superflow. We use the Keldysh technique in a curved space-time to develop a quantum geometric theory of fluctuations in superfluid hydrodynamics. This theory relies on a 'quantized' generalization of the two-fluid description of Landau and Khalatnikov, where the superfluid component is viewed as a quasi-classical field coupled to a normal component -- the collective modes/phonons representing a quantum bath. This relates the problem in the h…
Observation of brane parity order in programmable optical lattices
该研究在可编程光学晶格中实现二维Bose-Hubbard模型，通过单粒子量子行走验证系统性能，并在强关联区域实验证实膜奇偶序作为超流到莫特绝缘相变的非局域序参量。
We propose an ultracold atom analogue of early universe vacuum decay using all three states of a spin-1 Bose gas. We consider a one-dimensional system with both radio frequency and optical Raman coupling between internal states. An advantage of our proposal is the lack of a time-modulated coupling, which can lead to instabilities. Within the elaborate phase structure of the system we identify an effective Klein-Gordon field and use Gross-Pitaevskii simulations within the truncated Wigner approximation to model the decay of its false vacuum. We examine the dependence of the rate of vacuum decay…
We investigate the formation dynamics of sonic horizons in a Bose gas confined in a (quasi) one-dimensional trap. This system is one of the most promising realizations of the analogue gravity paradigm and has already been successfully studied experimentally. Taking advantage of the exact solution of the one-dimensional, hard-core, Bose model (Tonks-Girardeau gas) we show that, by switching on a step potential, either a sonic (black-hole-like) horizon or a black/white hole pair may form, according to the initial velocity of the fluid. Our simulations never suggest the formation of an isolated w…
Rotational superradiance is one of the most fascinating phenomena in black-hole physics. Here, with the aim of probing quantum properties of superradiance in the lab, we investigate the interaction of the acoustic waves with quantum vortices in Bose-Einstein condensates (BEC) in the framework of dissipative mean-field model. We find the conditions of the acoustic-induced quantum phase slips in condensates with ring topology and discuss the possibility of observing an acoustic analogue of quantum superradiance in ultracold atomic gases.
Gravitational Waves and Black Hole perturbations in Acoustic Analogues
本文利用玻色-爱因斯坦凝聚体中的流体力学/引力类比，提出通过外部势产生类引力波微扰来激发声学黑洞，使其通过声子发射实现弛豫。
Thermo-optic interaction significantly differs from the usual particle-particle interactions in physics, as it is retarded in time. A prominent platform for realising this kind of interaction are photon Bose-Einstein condensates, which are created in dye-filled microcavities. The dye solution continually absorbs and re-emits these photons, causing the photon gas to thermalise and to form a Bose-Einstein condensate. Because of a non-ideal quantum efficiency, these cycles heat the dye solution, creating a medium that provides an effective thermo-optic photon-photon interaction. So far, only a me…
We perform an analysis of the supercooled state in an analogue of an early universe phase transition based on a one dimensional, two-component Bose gas with time-dependent interactions. We demonstrate that the system behaves in the same way as a thermal, relativistic Bose gas undergoing a first order phase transition. We propose a way to prepare the state of the system in the metastable phase as an analogue to supercooling in the early universe. While we show that parametric resonances in the system can be suppressed by thermal damping, we find that the theoretically estimated thermal damping …
Anisotropic Inflation in Dipolar Bose-Einstein Condensates
本文提出利用偶极玻色-爱因斯坦凝聚体中声速的方向依赖性构建各向异性类比时空度规，模拟暴胀期间涨落谱的各向异性演化，并通过膨胀速度调控最终残余各向异性，为宇宙学研究提供可调谐的实验室量子模拟平台。
We discuss the possibility of emitting vector solitons from a two-component elongated BEC by manipulating in time the inter- or intra-species scattering lengths with Feshbach resonance tuning. We present different situations which do not have an analogue in the single species case. In particular, we show vector soliton out-coupling by tuning the interspecies forces, how the evolution in one species is controlled by tuning the dynamics of the other, and how one can implement the so-called supersolitons. The analysis is performed by numerical simulations of the one-dimensional Gross-Pitaevskii e…
We investigate the deformation of wavefronts of sound waves in rotating Bose-Einstein condensates. In irrational fluid flows Berry et al. identified this kind of deformation as the hydrodynamic analogue of the Aharonov-Bohm effect. We study this effect in Bose-Einstein condensates and obtain the Aharonov-Bohm phase shift at all wavelengths. We show that this deformation of wave fronts is seen in both phase and density fluctuations. For wavelengths larger than the healing length, the phase fluctuations experience a phase shift of the order of $2π$ times the winding number. We also consider latt…
A Maxwell Fish-Eye Lens in a Bose-Einstein Condensate
利用玻色-爱因斯坦凝聚体中的声子激发实验实现光学麦克斯韦鱼眼透镜类似物，通过调控声子实现变折射率，测量声子波前验证聚焦行为，为用超冷原子设计有效折射率等提供框架。
The stacks of Bose-Einstein condensates coupled by long Josephson junctions present a rich phenomenology feasible to experimental realization and specially suitable for technological applications as the nonlinear-optics and superconducting analogues have already proved. Among this, we show that transverse Bloch waves excited in arrays of one-dimensional coupled condensates can carry tunneling superflows whose dynamical stability depends on the quasimomentum. Across the stacks with periodic boundary conditions, forming closed ring-shaped systems, such Bloch states yield transverse Josephson vor…
Bogolon-mediated electromagnetic wave absorption in multicomponent Bose-Einstein condensates
本文研究了零温下两组分Bose-Einstein凝聚体中Bogolon介导的电磁波吸收过程，建立了微观理论并证明可通过调节凝聚体参数操控吸收特性。
Cold atomic gases of interacting bosons subject to rapid rotation and confined in anharmonic traps can theoretically exhibit analogues of the fractional quantum Hall effect for electrons in strong magnetic fields. In this setting the Coriolis force due to the rotation mimics the Lorentz force on charged particles but artificial gauge fields can also be obtained by coupling the internal structure of the atoms to light fields. The chapter discusses mathematical aspects of transitions to different strongly correlated phases that appear when the parameters of a model Hamiltonian are varied.
We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunc…
Inflationary Dynamics and Particle Production in a Toroidal Bose-Einstein Condensate
本研究理论分析膨胀环面BEC对暴胀宇宙的模拟，揭示声子红移、阻尼及自发粒子产生机制，并指出其在原子密度与关联中的观测信号。
Spin-orbit-coupled Bose-Einstein condensates (SOBECs) exhibit two new phases of matter, now known as the stripe and plane-wave phases. When two interacting spin components of a SOBEC spatially overlap, density modulations with periodicity given by the spin-orbit coupling strength appear. In equilibrium, these components fully overlap in the miscible stripe phase, and overlap only in a domain wall in the immiscible plane-wave phase. Here we probe the density modulation present in any overlapping region with optical Bragg scattering, and observe the sudden drop of Bragg scattering as the overlap…
The cosmological constant is one of the most pressing problems in modern physics. We address this issue from an emergent gravity standpoint, by using an analogue gravity model. Indeed, the dynamics of the emergent metric in a Bose-Einstein condensate can be described by a Poisson-like equation with a vacuum source term reminiscent of a cosmological constant. The direct computation of this term shows that in emergent gravity scenarios this constant may be naturally much smaller than the naive ground-state energy of the emergent effective field theory. This suggests that a proper computation of …
We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-1/2) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling $g_{\uparrow\downarrow}$ to the intracomponent one g>0. This time-reversal-invariant setting represents a bosonic analogue of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for $g_{\uparrow\downarrow}$ up to as l…
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