Cavity QED with a Bose-Einstein condensate

Cavity quantum electrodynamics (cavity QED) describes the coherent interaction between matter and an electromagnetic field confined within a resonator structure, and is providing a useful platform for developing concepts in quantum information processing. By using high-quality resonators, a strong coupling regime can be reached experimentally in which atoms coherently exchange a photon with a single light-field mode many times before dissipation sets in. This has led to fundamental studies with both microwave and optical resonators. To meet the challenges posed by quantum state engineering and quantum information processing, recent experiments have focused on laser cooling and trapping of atoms inside an optical cavity. However, the tremendous degree of control over atomic gases achieved with Bose-Einstein condensation has so far not been used for cavity QED. Here we achieve the strong coupling of a Bose-Einstein condensate to the quantized field of an ultrahigh-finesse optical cavity and present a measurement of its eigenenergy spectrum. This is a conceptually new regime of cavity QED, in which all atoms occupy a single mode of a matter-wave field and couple identically to the light field, sharing a single excitation. This opens possibilities ranging from quantum communication to a wealth of new phenomena that can be expected in the many-body physics of quantum gases with cavity-mediated interactions.     

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.     

Bose-Einstein condensation on a microelectronic chip

Although Bose-Einstein condensates of ultracold atoms have been experimentally realizable for several years, their formation and manipulation still impose considerable technical challenges. An all-optical technique that enables faster production of Bose-Einstein condensates was recently reported. Here we demonstrate that the formation of a condensate can be greatly simplified using a microscopic magnetic trap on a chip. We achieve Bose-Einstein condensation inside the single vapour cell of a magneto-optical trap in as little as 700 ms-more than a factor of ten faster than typical experiments, and a factor of three faster than the all-optical technique. A coherent matter wave is emitted normal to the chip surface when the trapped atoms are released into free fall; alternatively, we couple the condensate into an 'atomic conveyor belt', which is used to transport the condensed cloud non-destructively over a macroscopic distance parallel to the chip surface. The possibility of manipulating laser-like coherent matter waves with such an integrated atom-optical system holds promise for applications in interferometry, holography, microscopy, atom lithography and quantum information processing.     

Coherent zero-state and pi-state in an exciton-polariton condensate array

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix. The wavefunction of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena. The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium, superconducting Josephson junctions or atomic Bose-Einstein condensates. Under certain circumstances, a quantum phase difference of pi is predicted to develop among weakly coupled Josephson junctions. Such a meta-stable pi-state was discovered in a weak link of superfluid 3He, which is characterized by a 'p-wave' order parameter. The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed, but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.     

Many-particle entanglement with Bose-Einstein condensates

The possibility of creating and manipulating entangled states of systems of many particles is of significant interest for quantum information processing; such a capability could lead to new applications that rely on the basic principles of quantum mechanics. So far, up to four atoms have been entangled in a controlled way. A crucial requirement for the production of entangled states is that they can be considered pure at the single-particle level. Bose-Einstein condensates fulfil this requirement; hence it is natural to investigate whether they can also be used in some applications of quantum information. Here we propose a method to achieve substantial entanglement of a large number of atoms in a Bose-Einstein condensate. A single resonant laser pulse is applied to all the atoms in the condensate, which is then allowed to evolve freely; in this latter stage, collisional interactions produce entanglement between the atoms. The technique should be realizable with present technology.     

Nonlinear and quantum atom optics

Coherent matter waves in the form of Bose-Einstein condensates have led to the development of nonlinear and quantum atom optics - the de Broglie wave analogues of nonlinear and quantum optics with light. In nonlinear atom optics, four-wave mixing of matter waves and mixing of combinations of light and matter waves have been observed; such progress culminated in the demonstration of phase-coherent matter-wave amplification. Solitons represent another active area in nonlinear atom optics: these non-dispersing propagating modes of the equation that governs Bose-Einstein condensates have been created experimentally, and observed subsequently to break up into vortices. Quantum atom optics is concerned with the statistical properties and correlations of matter-wave fields. A first step in this area is the measurement of reduced number fluctuations in a Bose-Einstein condensate partitioned into a series of optical potential wells.     

Collapse and revival of the matter wave field of a Bose-Einstein condensate

A Bose-Einstein condensate represents the most 'classical' form of a matter wave, just as an optical laser emits the most classical form of an electromagnetic wave. Nevertheless, the matter wave field has a quantized structure owing to the granularity of the discrete underlying atoms. Although such a field is usually assumed to be intrinsically stable (apart from incoherent loss processes), this is no longer true when the condensate is in a coherent superposition of different atom number states. For example, in a Bose-Einstein condensate confined by a three-dimensional optical lattice, each potential well can be prepared in a coherent superposition of different atom number states, with constant relative phases between neighbouring lattice sites. It is then natural to ask how the individual matter wave fields and their relative phases evolve. Here we use such a set-up to investigate these questions experimentally, observing that the matter wave field of the Bose-Einstein condensate undergoes a periodic series of collapses and revivals; this behaviour is directly demonstrated in the dynamical evolution of the multiple matter wave interference pattern. We attribute the oscillations to the quantized structure of the matter wave field and the collisions between individual atoms.     

Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip

An optical cavity enhances the interaction between atoms and light, and the rate of coherent atom-photon coupling can be made larger than all decoherence rates of the system. For single atoms, this 'strong coupling regime' of cavity quantum electrodynamics has been the subject of many experimental advances. Efforts have been made to control the coupling rate by trapping the atom and cooling it towards the motional ground state; the latter has been achieved in one dimension so far. For systems of many atoms, the three-dimensional ground state of motion is routinely achieved in atomic Bose-Einstein condensates (BECs). Although experiments combining BECs and optical cavities have been reported recently, coupling BECs to cavities that are in the strong-coupling regime for single atoms has remained an elusive goal. Here we report such an experiment, made possible by combining a fibre-based cavity with atom-chip technology. This enables single-atom cavity quantum electrodynamics experiments with a simplified set-up and realizes the situation of many atoms in a cavity, each of which is identically and strongly coupled to the cavity mode. Moreover, the BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field; we demonstrate that this gives rise to a controlled, tunable coupling rate. We study the heating rate caused by a cavity transmission measurement as a function of the coupling rate and find no measurable heating for strongly coupled BECs. The spectrum of the coupled atoms-cavity system, which we map out over a wide range of atom numbers and cavity-atom detunings, shows vacuum Rabi splittings exceeding 20 gigahertz, as well as an unpredicted additional splitting, which we attribute to the atomic hyperfine structure. We anticipate that the system will be suitable as a light-matter quantum interface for quantum information.     

Observation of coherent optical information storage in an atomic medium using halted light pulses

Electromagnetically induced transparency is a quantum interference effect that permits the propagation of light through an otherwise opaque atomic medium; a 'coupling' laser is used to create the interference necessary to allow the transmission of resonant pulses from a 'probe' laser. This technique has been used to slow and spatially compress light pulses by seven orders of magnitude, resulting in their complete localization and containment within an atomic cloud. Here we use electromagnetically induced transparency to bring laser pulses to a complete stop in a magnetically trapped, cold cloud of sodium atoms. Within the spatially localized pulse region, the atoms are in a superposition state determined by the amplitudes and phases of the coupling and probe laser fields. Upon sudden turn-off of the coupling laser, the compressed probe pulse is effectively stopped; coherent information initially contained in the laser fields is 'frozen' in the atomic medium for up to 1 ms. The coupling laser is turned back on at a later time and the probe pulse is regenerated: the stored coherence is read out and transferred back into the radiation field. We present a theoretical model that reveals that the system is self-adjusting to minimize dissipative loss during the 'read' and 'write' operations. We anticipate applications of this phenomenon for quantum information processing.     

激光冷却和操控原子:原理与应用

 利用激光进行冷却和囚禁原子,可降低原子热运动速度、实现原子的量子操控,在精密测量等领域具有重要应用。本文概述了激光冷却和囚禁原子技术的发展历程及其基本原理,综述了该技术在玻色-爱因斯坦凝聚、原子钟和原子干涉仪等领域的应用。     

Dynamics of collapsing and exploding Bose-Einstein condensates.

When atoms in a gas are cooled to extremely low temperatures, they will-under the appropriate conditions-condense into a single quantum-mechanical state known as a Bose-Einstein condensate. In such systems, quantum-mechanical behaviour is evident on a macroscopic scale. Here we explore the dynamics of how a Bose-Einstein condensate collapses and subsequently explodes when the balance of forces governing its size and shape is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the interatomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally applied magnetic field yields detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wavefunction and oscillating remnant condensates that survive the collapse. All these processes have curious dependences on time, on the strength of the interaction and on the number of condensate atoms. Although the system would seem to be simple and well characterized, our measurements reveal many phenomena that challenge theoretical models.     

Spin-orbit-coupled Bose-Einstein condensates

Spin-orbit (SO) coupling--the interaction between a quantum particle's spin and its momentum--is ubiquitous in physical systems. In condensed matter systems, SO coupling is crucial for the spin-Hall effect and topological insulators; it contributes to the electronic properties of materials such as GaAs, and is important for spintronic devices. Quantum many-body systems of ultracold atoms can be precisely controlled experimentally, and would therefore seem to provide an ideal platform on which to study SO coupling. Although an atom's intrinsic SO coupling affects its electronic structure, it does not lead to coupling between the spin and the centre-of-mass motion of the atom. Here, we engineer SO coupling (with equal Rashba and Dresselhaus strengths) in a neutral atomic Bose-Einstein condensate by dressing two atomic spin states with a pair of lasers. Such coupling has not been realized previously for ultracold atomic gases, or indeed any bosonic system. Furthermore, in the presence of the laser coupling, the interactions between the two dressed atomic spin states are modified, driving a quantum phase transition from a spatially spin-mixed state (lasers off) to a phase-separated state (above a critical laser intensity). We develop a many-body theory that provides quantitative agreement with the observed location of the transition. The engineered SO coupling--equally applicable for bosons and fermions--sets the stage for the realization of topological insulators in fermionic neutral atom systems.     

Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate

A central goal in condensed matter and modern atomic physics is the exploration of quantum phases of matter--in particular, how the universal characteristics of zero-temperature quantum phase transitions differ from those established for thermal phase transitions at non-zero temperature. Compared to conventional condensed matter systems, atomic gases provide a unique opportunity to explore quantum dynamics far from equilibrium. For example, gaseous spinor Bose-Einstein condensates (whose atoms have non-zero internal angular momentum) are quantum fluids that simultaneously realize superfluidity and magnetism, both of which are associated with symmetry breaking. Here we explore spontaneous symmetry breaking in 87Rb spinor condensates, rapidly quenched across a quantum phase transition to a ferromagnetic state. We observe the formation of spin textures, ferromagnetic domains and domain walls, and demonstrate phase-sensitive in situ detection of spin vortices. The latter are topological defects resulting from the symmetry breaking, containing non-zero spin current but no net mass current.     

Sideband cooling of micromechanical motion to the quantum ground state

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems, fuelling progress towards quantum computing with trapped ions and generating new states of matter with Bose-Einstein condensates. Analogous cooling techniques can provide a general and flexible method of preparing macroscopic objects in their motional ground state. Cavity optomechanical or electromechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime--in which a system has less than a single quantum of motion--has been difficult because sideband cooling has not sufficiently overwhelmed the coupling of low-frequency mechanical systems to their hot environments. Here we demonstrate sideband cooling of an approximately 10-MHz micromechanical oscillator to the quantum ground state. This achievement required a large electromechanical interaction, which was obtained by embedding a micromechanical membrane into a superconducting microwave resonant circuit. To verify the cooling of the membrane motion to a phonon occupation of 0.34?±?0.05 phonons, we perform a near-Heisenberg-limited position measurement within (5.1?±?0.4)h/2π, where h is Planck's constant. Furthermore, our device exhibits strong coupling, allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass. Because mechanical oscillators can couple to light of any frequency, they could also serve as a unique intermediary for transferring quantum information between microwave and optical domains.     

Skyrmions in a ferromagnetic Bose-Einstein condensate.

Multi-component Bose-Einstein condensates provide opportunities to explore experimentally the wealth of physics associated with the spin degrees of freedom. The ground-state properties and line-like vortex excitations of these quantum systems have been studied theoretically. In principle, nontrivial spin textures consisting of point-like topological excitations, or skyrmions, could exist in a multi-component Bose-Einstein condensate, owing to the superfluid nature of the gas. Although skyrmion excitations are already known in the context of nuclear physics and the quantum-Hall effect, creating these excitations in an atomic condensate would offer an opportunity to study their physical behaviour in much greater detail, while also enabling an ab initio comparison between theory and experiment. Here we investigate theoretically the stability of skyrmions in a fictitious spin-1/2 condensate of 87Rb atoms. We find that skyrmions can exist in such a gas only as a metastable state, but with a lifetime comparable to (or even longer than) the typical lifetime of the condensate itself.     

Raman型原子激光制备过程中光场的压缩特性

研究了Raman型原子激光制备过程中探测光场的压缩特性．这种原子激光是利用钠原子玻色-爱因斯坦凝聚体（BEC）与一束较弱的压缩相干态探测光和一束较强的经典泵浦光Raman跃迁相互作用制备得到的研究结果表明,压缩相干态探测光在原子激光制备过程中呈现周期性压缩,其压缩周期与原子阱中的平均原子数、光场与原子BEC相互作用强度及光场的失谐量等因素有关,压缩深度决定于探测光场的初始压缩因子．     

A quantum scattering interferometer

The collision of two ultracold atoms results in a quantum mechanical superposition of the two possible outcomes: each atom continues without scattering, and each atom scatters as an outgoing spherical wave with an s-wave phase shift. The magnitude of the s-wave phase shift depends very sensitively on the interaction between the atoms. Quantum scattering and the underlying phase shifts are vitally important in many areas of contemporary atomic physics, including Bose-Einstein condensates, degenerate Fermi gases, frequency shifts in atomic clocks and magnetically tuned Feshbach resonances. Precise experimental measurements of quantum scattering phase shifts have not been possible because the number of scattered atoms depends on the s-wave phase shifts as well as the atomic density, which cannot be measured precisely. Here we demonstrate a scattering experiment in which the quantum scattering phase shifts of individual atoms are detected using a novel atom interferometer. By performing an atomic clock measurement using only the scattered part of each atom's wavefunction, we precisely measure the difference of the s-wave phase shifts for the two clock states in a density-independent manner. Our method will enable direct and precise measurements of ultracold atom-atom interactions, and may be used to place stringent limits on the time variations of fundamental constants.     

Bose-Einstein condensation of atomic gases

The early experiments on Bose-Einstein condensation in dilute atomic gases accomplished three long-standing goals. First, cooling of neutral atoms into their motional ground state, thus subjecting them to ultimate control, limited only by Heisenberg's uncertainty relation. Second, creation of a coherent sample of atoms, in which all occupy the same quantum state, and the realization of atom lasers - devices that output coherent matter waves. And third, creation of a gaseous quantum fluid, with properties that are different from the quantum liquids helium-3 and helium-4. The field of Bose-Einstein condensation of atomic gases has continued to progress rapidly, driven by the combination of new experimental techniques and theoretical advances. The family of quantum-degenerate gases has grown, and now includes metastable and fermionic atoms. Condensates have become an ultralow-temperature laboratory for atom optics, collisional physics and many-body physics, encompassing phonons, superfluidity, quantized vortices, Josephson junctions and quantum phase transitions.     

Atom-molecule coherence in a Bose-Einstein condensate

Recent advances in the precise control of ultracold atomic systems have led to the realisation of Bose Einstein condensates (BECs) and degenerate Fermi gases. An important challenge is to extend this level of control to more complicated molecular systems. One route for producing ultracold molecules is to form them from the atoms in a BEC. For example, a two-photon stimulated Raman transition in a (87)Rb BEC has been used to produce (87)Rb(2) molecules in a single rotational-vibrational state, and ultracold molecules have also been formed through photoassociation of a sodium BEC. Although the coherence properties of such systems have not hitherto been probed, the prospect of creating a superposition of atomic and molecular condensates has initiated much theoretical work. Here we make use of a time-varying magnetic field near a Feshbach resonance to produce coherent coupling between atoms and molecules in a (85)Rb BEC. A mixture of atomic and molecular states is created and probed by sudden changes in the magnetic field, which lead to oscillations in the number of atoms that remain in the condensate. The oscillation frequency, measured over a large range of magnetic fields, is in excellent agreement with the theoretical molecular binding energy, indicating that we have created a quantum superposition of atoms and diatomic molecules two chemically different species.     

Controlled exchange interaction between pairs of neutral atoms in an optical lattice

Ultracold atoms trapped by light offer robust quantum coherence and controllability, providing an attractive system for quantum information processing and for the simulation of complex problems in condensed matter physics. Many quantum information processing schemes require the manipulation and deterministic entanglement of individual qubits; this would typically be accomplished using controlled, state-dependent, coherent interactions among qubits. Recent experiments have made progress towards this goal by demonstrating entanglement among an ensemble of atoms confined in an optical lattice. Until now, however, there has been no demonstration of a key operation: controlled entanglement between atoms in isolated pairs. Here we use an optical lattice of double-well potentials to isolate and manipulate arrays of paired (87)Rb atoms, inducing controlled entangling interactions within each pair. Our experiment realizes proposals to use controlled exchange coupling in a system of neutral atoms. Although 87Rb atoms have nearly state-independent interactions, when we force two atoms into the same physical location, the wavefunction exchange symmetry of these identical bosons leads to state-dependent dynamics. We observe repeated interchange of spin between atoms occupying different vibrational levels, with a coherence time of more than ten milliseconds. This observation demonstrates the essential component of a neutral atom quantum SWAP gate (which interchanges the state of two qubits). Its 'half-implementation', the root SWAP gate, is entangling, and together with single-qubit rotations it forms a set of universal gates for quantum computation.