Observation of the ideal Josephson effect in superfluid 4He

Superfluids and superconductors are the only states of condensed matter that can be described by a single wavefunction, with a coherent quantum phase Phi. The mass flow in a superfluid can be described by classical hydrodynamics for small flow velocity, but above a critical velocity, quantized vortices are created and the classical picture breaks down. This can be observed for a superfluid flowing through a microscopic aperture when the mass flow is measured as a function of the phase difference across the aperture; the curve resembles a hysteretic sawtooth where each jump corresponds to the creation of a vortex. When the aperture is made small enough, the system can enter the so-called 'ideal' Josephson regime, where the superfluid mass flow becomes a continuous function of the phase difference. This regime has been detected in superfluid 3He, but was hitherto believed to be unobservable, owing to fluctuations, in 4He. Here we report the observation of the ideal Josephson effect in 4He. We study the flow of 4He through an array of micro-apertures and observe a transition to the ideal Josephson regime as the temperature is increased towards the superfluid transition temperature, Tlambda.     

Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas

Any state of matter is classified according to its order, and the type of order that a physical system can possess is profoundly affected by its dimensionality. Conventional long-range order, as in a ferromagnet or a crystal, is common in three-dimensional systems at low temperature. However, in two-dimensional systems with a continuous symmetry, true long-range order is destroyed by thermal fluctuations at any finite temperature. Consequently, for the case of identical bosons, a uniform two-dimensional fluid cannot undergo Bose-Einstein condensation, in contrast to the three-dimensional case. However, the two-dimensional system can form a 'quasi-condensate' and become superfluid below a finite critical temperature. The Berezinskii-Kosterlitz-Thouless (BKT) theory associates this phase transition with the emergence of a topological order, resulting from the pairing of vortices with opposite circulation. Above the critical temperature, proliferation of unbound vortices is expected. Here we report the observation of a BKT-type crossover in a trapped quantum degenerate gas of rubidium atoms. Using a matter wave heterodyning technique, we observe both the long-wavelength fluctuations of the quasi-condensate phase and the free vortices. At low temperatures, the gas is quasi-coherent on the length scale set by the system size. As the temperature is increased, the loss of long-range coherence coincides with the onset of proliferation of free vortices. Our results provide direct experimental evidence for the microscopic mechanism underlying the BKT theory, and raise new questions regarding coherence and superfluidity in mesoscopic systems.     

Magnetic and non-magnetic phases of a quantum spin liquid

A quantum spin-liquid phase is an intriguing possibility for a system of strongly interacting magnetic units in which the usual magnetically ordered ground state is avoided owing to strong quantum fluctuations. It was first predicted theoretically for a triangular-lattice model with antiferromagnetically coupled S = 1/2 spins. Recently, materials have become available showing persuasive experimental evidence for such a state. Although many studies show that the ideal triangular lattice of S = 1/2 Heisenberg spins actually orders magnetically into a three-sublattice, non-collinear 120° arrangement, quantum fluctuations significantly reduce the size of the ordered moment. This residual ordering can be completely suppressed when higher-order ring-exchange magnetic interactions are significant, as found in nearly metallic Mott insulators. The layered molecular system κ-(BEDT-TTF)(2)Cu(2)(CN)(3) is a Mott insulator with an almost isotropic, triangular magnetic lattice of spin-1/2 BEDT-TTF dimers that provides a prime example of a spin liquid formed in this way. Despite a high-temperature exchange coupling, J, of 250 K (ref. 6), no obvious signature of conventional magnetic ordering is seen down to 20 mK (refs 7, 8). Here we show, using muon spin rotation, that applying a small magnetic field to this system produces a quantum phase transition between the spin-liquid phase and an antiferromagnetic phase with a strongly suppressed moment. This can be described as Bose-Einstein condensation of spin excitations with an extremely small spin gap. At higher fields, a second transition is found that suggests a threshold for deconfinement of the spin excitations. Our studies reveal the low-temperature magnetic phase diagram and enable us to measure characteristic critical properties. We compare our results closely with current theoretical models, and this gives some further insight into the nature of the spin-liquid phase.     

Evidence for superfluidity of ultracold fermions in an optical lattice

The study of superfluid fermion pairs in a periodic potential has important ramifications for understanding superconductivity in crystalline materials. By using cold atomic gases, various models of condensed matter can be studied in a highly controllable environment. Weakly repulsive fermions in an optical lattice could undergo d-wave pairing at low temperatures, a possible mechanism for high temperature superconductivity in the copper oxides. The lattice potential could also strongly increase the critical temperature for s-wave superfluidity. Recent experimental advances in bulk atomic gases include the observation of fermion-pair condensates and high-temperature superfluidity. Experiments with fermions and bosonic bound pairs in optical lattices have been reported but have not yet addressed superfluid behaviour. Here we report the observation of distinct interference peaks when a condensate of fermionic atom pairs is released from an optical lattice, implying long-range order (a property of a superfluid). Conceptually, this means that s-wave pairing and coherence of fermion pairs have now been established in a lattice potential, in which the transport of atoms occurs by quantum mechanical tunnelling and not by simple propagation. These observations were made for interactions on both sides of a Feshbach resonance. For larger lattice depths, the coherence was lost in a reversible manner, possibly as a result of a transition from superfluid to insulator. Such strongly interacting fermions in an optical lattice can be used to study a new class of hamiltonians with interband and atom-molecule couplings.     

Phase-slip-induced dissipation in an atomic Bose-Hubbard system

Phase-slips control dissipation in many bosonic systems, determining the critical velocity of superfluid helium and the generation of resistance in thin superconducting wires. Technological interest has been largely motivated by applications involving nanoscale superconducting circuit elements, such as standards based on quantum phase-slip junctions. Although phase slips caused by thermal fluctuations at high temperatures are well understood, controversy remains over the role of phase slips in small-scale superconductors--in solids, problems such as uncontrolled noise sources and disorder complicate their study and application. Here we show that phase slips can lead to dissipation in a clean and well-characterized Bose-Hubbard system, by experimentally studying the transport of ultracold atoms trapped in an optical lattice. In contrast to previous work, we explore a low-velocity regime described by the three-dimensional Bose-Hubbard model that is unaffected by instabilities, and we measure the effect of temperature on the dissipation strength. The damping rate of atomic motion (the analogue of electrical resistance in a solid) in the confining parabolic potential is well fitted by a model that includes finite damping at zero temperature. The low-temperature behaviour is consistent with the theory of quantum tunnelling of phase slips, whereas at higher temperatures a crossover consistent with a transition to thermal activation of phase slips is evident. Motion-induced features reminiscent of vortices and vortex rings associated with phase slips are also observed in time-of-flight imaging. These results clarify the role of phase slips in superfluid systems. They may also be of relevance in understanding the source of metallic phases observed in thin films, or serve as a test bed for theories of bosonic dissipation based upon variants of the Bose-Hubbard model.     

横磁场中各向同性XY链的基态纠缠研究

分析了横磁场中各向同性XY自旋链的基态能量和纠缠问题。研究发现,三量子比特系统中存在一个相变点,此点上,基态能量和纠缠可发生量子相变,基态从W态进入非纠缠;而四量子比特系统存在两个相变点,基态的能量和纠缠均可在相变点处发生量子相变,使纠缠性质发生改变。随着磁场强度的增大,基态纠缠逐渐减小,直到完全消失。四比特系统纠缠的减小要比三比特系统纠缠减小的速度缓慢。     

Phase diagram of a two-component Fermi gas with resonant interactions

The pairing of fermions lies at the heart of superconductivity and superfluidity. The stability of these pairs determines the robustness of the superfluid state, and the quest for superconductors with high critical temperature equates to a search for systems with strong pairing mechanisms. Ultracold atomic Fermi gases present a highly controllable model system for studying strongly interacting fermions. Tunable interactions (through Feshbach collisional resonances) and the control of population or mass imbalance among the spin components provide unique opportunities to investigate the stability of pairing-and possibly to search for exotic forms of superfluidity. A major controversy has surrounded the stability of superfluidity against an imbalance between the two spin components when the fermions interact resonantly (that is, at unitarity). Here we present the phase diagram of a spin-polarized Fermi gas of (6)Li atoms at unitarity, experimentally mapping out the superfluid phases versus temperature and density imbalance. Using tomographic techniques, we reveal spatial discontinuities in the spin polarization; this is the signature of a first-order superfluid-to-normal phase transition, and disappears at a tricritical point where the nature of the phase transition changes from first-order to second-order. At zero temperature, there is a quantum phase transition from a fully paired superfluid to a partially polarized normal gas. These observations and the implementation of an in situ ideal gas thermometer provide quantitative tests of theoretical calculations on the stability of resonant superfluidity.     

反绝热极限下MX链晶体中的量子晶格涨落效应:费米子自旋1/2态

相转变和对称破缺电荷密度波态的稳定性等物理特性决定于ＭＸ链系统的准一维、电子跃迁、电子－声子耦合和电子－电子相互作用。为讨论费米子自旋态ＭＸ 链系统的量子晶格涨落效应,从紧束缚Ｈａｍｉｌｔｏｎｉｓｎ模型出发,在反绝热极限条件下,采用Ｈａｒｔｒｅｅ－Ｆｏｃｋ近似,对ＭＸ链系统的电荷密度波序参量,绝缘相能隙,基态能量等进行了研究,并得到确定绝缘相能隙的自洽解方程。计算结果表明,在反绝热极限条件下,绝缘相能隙随电声子耦合强度的增大而增大,当电声子耦合强度达到临界值时,系统发生二聚化相变。     

Coherent singlet-triplet oscillations in a silicon-based double quantum dot

Silicon is more than the dominant material in the conventional microelectronics industry: it also has potential as a host material for emerging quantum information technologies. Standard fabrication techniques already allow the isolation of single electron spins in silicon transistor-like devices. Although this is also possible in other materials, silicon-based systems have the advantage of interacting more weakly with nuclear spins. Reducing such interactions is important for the control of spin quantum bits because nuclear fluctuations limit quantum phase coherence, as seen in recent experiments in GaAs-based quantum dots. Advances in reducing nuclear decoherence effects by means of complex control still result in coherence times much shorter than those seen in experiments on large ensembles of impurity-bound electrons in bulk silicon crystals. Here we report coherent control of electron spins in two coupled quantum dots in an undoped Si/SiGe heterostructure and show that this system has a nuclei-induced dephasing time of 360 nanoseconds, which is an increase by nearly two orders of magnitude over similar measurements in GaAs-based quantum dots. The degree of phase coherence observed, combined with fast, gated electrical initialization, read-out and control, should motivate future development of silicon-based quantum information processors.     

晶格量子涨落对正方晶格反铁磁海森堡模型基态的影响

从正方晶格反铁磁海森堡模型出发,应用正则变换方法讨论了非绝热近似下晶格量子涨落对系统基态的影响．计算结果表明,自旋－声子耦合相互作用可以使系统建立一个新的稳定基态．在此基态中,系统的能量可以得到明显的降低,而且有小的交错磁序存在．     

相干光场的相对相位对K-型五能级原子的单光子和双光子吸收性质的影响

当K-型五能级原子的两基态能级邻近简并时,连接基态的两个跃迁路径与同一个真空场辐射场相互作用导致的量子干涉效应便产生了空场诱导相干性。K-型五能级原子系统的单光子和双光子电磁诱导透明受空场诱导相干性的作用效果十分明显,单光子吸收性质与外加相干光场的相对相位也有直接联系。     

Scaling of entanglement close to a quantum phase transition

Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant, and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems, localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor-insulator transition in two-dimensional systems. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement, is the resource that enables quantum computation and communication. The role of entanglement at a phase transition is not captured by statistical mechanics-a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.     

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.     

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.     

Observation of squeezed light from one atom excited with two photons

Single quantum emitters such as atoms are well known as non-classical light sources with reduced noise in the intensity, capable of producing photons one by one at given times. However, the light field emitted by a single atom can exhibit much richer dynamics. A prominent example is the predicted ability of a single atom to produce quadrature-squeezed light, which has fluctuations of amplitude or phase that are below the shot-noise level. However, such squeezing is much more difficult to observe than the emission of single photons. Squeezed beams have been generated using macroscopic and mesoscopic media down to a few tens of atoms, but despite experimental efforts, single-atom squeezing has so far escaped observation. Here we generate squeezed light with a single atom in a high-finesse optical resonator. The strong coupling of the atom to the cavity field induces a genuine quantum mechanical nonlinearity, which is several orders of magnitude larger than in typical macroscopic media. This produces observable quadrature squeezing, with an excitation beam containing on average only two photons per system lifetime. In sharp contrast to the emission of single photons, the squeezed light stems from the quantum coherence of photon pairs emitted from the system. The ability of a single atom to induce strong coherent interactions between propagating photons opens up new perspectives for photonic quantum logic with single emitters.     

Non-equilibrium coherence dynamics in one-dimensional Bose gases

Low-dimensional systems provide beautiful examples of many-body quantum physics. For one-dimensional (1D) systems, the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly interacting regimes. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1D Bose gases. Dynamic splitting is used to create two 1D systems in a phase coherent state. The time evolution of the coherence is revealed through local phase shifts of the subsequently observed interference patterns. Completely isolated 1D Bose gases are observed to exhibit universal sub-exponential coherence decay, in excellent agreement with recent predictions. For two coupled 1D Bose gases, the coherence factor is observed to approach a non-zero equilibrium value, as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase-locking two lasers by injection. The non-equilibrium dynamics of superfluids has an important role in a wide range of physical systems, such as superconductors, quantum Hall systems, superfluid helium and spin systems. Our experiments studying coherence dynamics show that 1D Bose gases are ideally suited for investigating this class of phenomena.     

Quantum phase transition in a single-molecule quantum dot

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots. Our work may offer new directions in terms of control and tunability for molecular spintronics.     

价转移金属络合物低温半导体—金属相变的计算机MONTE CARLO量子格点模拟

对价转移金属络合物材料低温条件下的半导体—金属态转变特性,采用计算机Monte Carlo技术,在Wannier表象中,对由位移变换和基态平均得到的多维序参量和状态参量量子统计平均方程组,进行Monte Carlo自洽迭代量子格点模拟,得到了系统的相图和序参量变化关系。     

Using photoemission spectroscopy to probe a strongly interacting Fermi gas

Ultracold atomic gases provide model systems in which to study many-body quantum physics. Recent experiments using Fermi gases have demonstrated a phase transition to a superfluid state with strong interparticle interactions. This system provides a realization of the 'BCS-BEC crossover' connecting the physics of Bardeen-Cooper-Schrieffer (BCS) superconductivity with that of Bose-Einstein condensates (BECs). Although many aspects of this system have been investigated, it has not yet been possible to measure the single-particle excitation spectrum (a fundamental property directly predicted by many-body theories). Here we use photoemission spectroscopy to directly probe the elementary excitations and energy dispersion in a strongly interacting Fermi gas of (40)K atoms. In the experiments, a radio-frequency photon ejects an atom from the strongly interacting system by means of a spin-flip transition to a weakly interacting state. We measure the occupied density of single-particle states at the cusp of the BCS-BEC crossover and on the BEC side of the crossover, and compare these results to that for a nearly ideal Fermi gas. We show that, near the critical temperature, the single-particle spectral function is dramatically altered in a way that is consistent with a large pairing gap. Our results probe the many-body physics in a way that could be compared to data for the high-transition-temperature superconductors. As in photoemission spectroscopy for electronic materials, our measurement technique for ultracold atomic gases directly probes low-energy excitations and thus can reveal excitation gaps and/or pseudogaps. Furthermore, this technique can provide an analogue of angle-resolved photoemission spectroscopy for probing anisotropic systems, such as atoms in optical lattice potentials.     

Squeezing and entanglement in a Bose-Einstein condensate

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means. This results in the standard quantum limit, which is reached in today's best available sensors of various quantities such as time and position. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states) at the two input ports. Bose-Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.