In this Letter, we report the first experimental realization and investigation of a spin-orbit coupled Fermi gas. Both spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state are observed as hallmarks of spin-orbit coupling in a Fermi gas. The single particle dispersion is mapped out by using momentum-resolved radio-frequency spectroscopy. From momentum distribution and momentum-resolved radio-frequency spectroscopy, we observe the change of fermion population in different helicity branches consistent with a finite temperature calculation, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system.

Spin-orbit coupling (SOC) is central to many physical phenomena, including fine structures of atomic spectra and topological phases in ultracold atoms. Whereas, in general, SOC is fixed in a system, laser-atom interaction provides a means to create and control synthetic SOC in ultracold atoms 1 . Despite significant experimental progress in this area 2-8 , two-dimensional (2D) synthetic SOC, which is crucial for exploring two-and threedimensional topological phases, is lacking. Here, we report the experimental realization of 2D SOC in ultracold 40 K Fermi gases using three lasers, each of which dresses one atomic hyperfine spin state. Through spin-injection radiofrequency (rf) spectroscopy 4 , we probe the spin-resolved energy dispersions of the dressed atoms, and observe a highly controllable Dirac point created by the 2D SOC. These results constitute a step towards the realization of new topological states of matter.There have been many theoretical proposals for creating multi-dimensional SOC in ultracold atoms 9-14 , so as to access novel macroscopic quantum phenomena and quantum topological states [15][16][17][18][19][20][21][22][23][24] . Whereas these proposals have not been realized in laboratories, physicists have also just begun to explore topological phenomena in optical lattices [25][26][27][28] . Here, we use the Raman scheme to produce a highly controllable 2D synthetic SOC for an ultracold Fermi gas of 40 K. Such SOC allows us to create and manipulate a single stable Dirac point on a 2D plane, which is detected by spin-injection rf spectroscopy 4 .We apply three far-detuned lasers propagating on the x-y plane to couple three ground hyperfine spin states, within the 4 2 S 1/2 ground electronic manifold, |1 = |F = 9/2, m F = 3/2 , |2 = |F = 9/2, m F = 1/2 and |3 = |F = 7/2, m F = 1/2 , where (F, m F ) are the quantum numbers for hyperfine spin states as shown in Fig. 1a, to the electronically excited states. Unlike the tripod scheme, where a single excited state is considered [9][10][11][15][16][17][18] , in the 40 K used here the excited states include a fine-structure doublet 4 2 P 1/2 (D 1 line) and 4 2 P 3/2 (D 2 line) with a finestructure splitting of ∼3.4 nm. Each of two D-line components also has hyperfine structures. After adiabatically eliminating excited states, the ring scheme proposed in ref. 12 is realized for three cyclically coupled states, with a generalization to arbitrary laser configurations. The Hamiltonian is written as( 1) where p denotes the momentum of atoms, k i (|k i | = 2π/λ i ) and ω i are the wavevectors and frequencies of the three lasers, Ω i are the Rabi frequencies, i, j are the indices for the three ground hyperfine spin and the excited states respectively, ε i and E j are the ground and excited state energies, n is the total number of the excited states and M ij is the matrix element of the dipole transition. Different from refs 9,10,15, each hyperfine ground spin state here is dressed by only one laser field, regardless of the excited states it is coupled to. A gau...

By exploiting recent developments associated with coupled microcavities, we introduce the concept of PT -symmetric phonon laser with balanced gain and loss. This is accomplished by introducing gain to one of the microcavities such that it balances the passive loss of the other. In the vicinity of the gain-loss balance, a strong nonlinear relation emerges between the intracavity photon intensity and the input power. This then leads to a giant enhancement of both optical pressure and mechanical gain, resulting in a highly efficient phonon-lasing action. These results provide a promising approach for manipulating optomechanical systems through PT -symmetric concepts. Potential applications range from enhancing mechanical cooling to designing phonon-laser amplifiers.PACS numbers: 03.75.Pp, 03.70.+k Recent advances in materials science and nanofabrication have led to spectacular achievements in cooling classical mechanical objects into the subtle quantum regime (e.g., [1][2][3][4]). These results are having a profound impact on a wide range of research topics, from probing basic rules of classical-to-quantum transitions [4][5][6][7] to creating novel devices operating in the quantum regime, e.g. ultra-weak force sensors [8] or electric-to-optical wave transducers [9,10]. The emerging field of cavity optomechanics (COM) [1] is also experiencing rapid evolution that is driven by studies aimed at understanding the underlying physics and by the fabrication of novel structures and devices enabled by recent developments in nanotechnology.The basic COM system includes a single resonator, where a highly-efficient energy transfer between the mechanical mode and intracavity photons is enabled by detuning an input laser from the cavity resonance [1]. A new extension, closely related to the present study, is the photonic molecule or compound microresonators [11][12][13], where a tunable optical tunneling can be exploited to bypass the frequency detuning requirement [12]. More strikingly, in this architecture, an analogue of two-level optical laser is provided by phonon-mediated transitions between two optical supermodes [13]. This phonon laser [13,14] provides the core technology to integrate coherent phonon sources, detectors, and waveguides -allowing the study of nonlinear phononics [15] and the operation of functional phononic devices [16].In parallel to these works, intense interest has also emerged recently in PT -symmetric optics [17][18][19]. A variety of optical structures, whose behaviors can be described by parity-time (PT ) symmetric Hamiltonians, have been fabricated [17]. These exotic structures provide unconventional and previously-unattainable control of light [1,18,19,21]. In very recent work, by manipulating the gain (in one active or externally-pumped resonator) to loss (in the other, passive, one) ratio, Ref.[1] realized an optical compound structure with remarkable PT -symmetric features, e.g. field localization in the active resonator and accompanied enhancement of optical nonlinearity leading to nonreci...

Quantum teleportation and quantum dense coding are two typical examples to exploit nonlocal quantum correlation of entangled states in quantum information to perform otherwise impossible tasks. Quantum teleportation is the disembodied transport of an unknown quantum state from one place to another 1 . Quantum dense coding provide a method by which two bits of classical information can be transmitted by sending one qubit of quantum information 2 . Discrete and continuous variable teleportations have been performed experimentally for single-photon polarization

We propose a scheme for transferring quantum states from the propagating light fields to macroscopic, collective vibrational degree of freedom of a massive mirror by exploiting radiation pressure effects. This scheme may prepare an Einstein-Podolsky-Rosen state in position and momentum of a pair of distantly separated movable mirrors by utilizing the entangled light fields produced from a nondegenerate optical parametric amplifier.

We present a continuous-variable ͑CV͒ Gaussian analog of cluster states, a new class of CV multipartite entangled states that can be generated from squeezing and quantum nondemolition coupling H I = ប X A X B . The entanglement properties of these states are studied in terms of classical communication and local operations. The graph states as general forms of the cluster states are presented. A chain for a one-dimensional example of cluster states can be readily experimentally produced only with squeezed light and beam splitters.

A tripartite entangled state of bright optical field is experimentally produced using an Einstein-Podolsky-Rosen entangled state for continuous variables and linear optics. The controlled dense coding among a sender, a receiver and a controller is demonstrated by exploiting the tripartite entanglement. The obtained three-mode position correlation and relative momentum correlation between the sender and the receiver and thus the improvements of the measured signal to noise ratios of amplitude and phase signals with respect to the shot noise limit are 3.28dB and 3.18dB respectively. If the mean photon number n equals 11 the channel capacity can be controllably inverted between 2.91 and 3.14. When n is larger than 1.0 and 10.52 the channel capacities of the controlled dense coding exceed the ideal single Quantum entanglement shared by more than two parties is the essential base for developing quantum communication network and quantum computation. The threeparticle entangled states for discrete variables, called also Greenberger-Horne-Zeilinger (GHZ) states, have been proposed [1] and then experimentally realized with optical system consisting of nonlinear (χ 2 ) crystal, pulse laser and linear optical elements [2] and with nuclear magnetic resonance [3]. The controlled dense coding for discrete variables using a three-particle entangled state has been proposed [4]. Recently, under the motivation of the successful experiments on continuous-variable quantum teleportation [5] and quantum dense coding [6], the schemes demonstrating quantum teleportation network [7] and controlled dense coding [8] for quantum variables with a continuous spectrum using multipartite entanglement have been theoretically proposed. So far to the best of our knowledges, the experimental report on the generation of multipartite entangled states for continuous variables and its application has not been presented.In this paper we report the first experimental demonstration of quantum entanglement among more than two quantum systems with continuous spectra. The tripartite entangled state is produced by distributing a twomode squeezed state light to three parties using linear optics. The obtained tripartite entangled optical beams are distributed to a sender (Alice), a receiver (Bob) and a controller (Claire) respectively. The information transmission capacity of the quantum channel between Alice and Bob is controlled by Claire. The channel capacity accomplished under Claire's help is always larger than that without his help. For the large mean photon number(n > 10.52), the channel capacity of the controlled dense coding communication exceeds that of ideal squeezed state communication. Fig.1 is the schematic of the experimental setup for tripartite entanglement generation and controlled dense coding. A semimonolithic nondegenerate optical parameter amplifier (NOPA) involving an α-cut type-II KTP crystal and pumped by an intracavity frequency-doubled and frequency-stabilized Nd:YAP/KTP laser serves as the initial bipartite entanglement source. The ...

We investigate the nonlinear interaction between a squeezed cavity mode and a mechanical mode in an optomechanical system (OMS) that allows us to selectively obtain either a radiation-pressure coupling or a parametric-amplification process. The squeezing of the cavity mode can enhance the interaction strength into the single-photon strong-coupling regime, even when the OMS is originally in the weak-coupling regime. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a broadband-squeezed vacuum environment that is phase-matched with the parametric amplification that squeezes the cavity mode. This proposal offers an alternative approach to control OMS using a squeezed cavity mode, which should allow single-photon quantum processes to be implemented with currently available optomechanical technology. Potential applications range from engineering single-photon sources to nonclassical phonon states. Cavity optomechanics has progressed enormously in recent years [1], with achievements including cooling of mechanical modes to their quantum ground states [2,3], demonstration of optomechanically-induced transparency [4,5], coherent state transfer between cavity and mechanical modes [6][7][8][9], and the realization of squeezed light [10][11][12]. In these experiments, a strong linearized optomechanical coupling is obtained under the condition of strong optical driving. However, the intrinsic nonlinearity of the radiation-pressure coupling in these OMSs is negligible [13][14][15][16][17][18][19].To explore the intrinsic nonlinearity of the optomechanical interaction, much theoretical research has recently focused on the single-photon strong-coupling regime, where the single-photon optomechanicalcoupling strength g 0 exceeds the cavity decay rate κ. In this regime, several interesting single-photon quantum processes are predicted, for both the optical and the mechanical modes. For example: photon blockade, the preparation of the nonclassical states of the optical and mechanical modes, multi-phonon sidebands, and quantum state reconstruction of the mechanical oscillator [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. However, these effects have not yet been realized experimentally due to the intrinsically weak radiation-pressure coupling in current OMSs, i.e., g 0 κ. To achieve g 0 ∼ κ, it has been proposed to use the collective mechanical modes in transmissive scatter arrays [35,36]. The ratio g 0 /κ may also be increased in superconducting circuits using the Josephson effect, but such devices are limited to electromechanical systems [37][38][39]. Moreover, postselected weak measurements [40] and optical coalescence [41] could also be used to increase the effective linear and quadratic optomechanical interactions, respectively.Here we present a method to reach the single-photon strong-coupling regime in an OMS, which is originally in the weak-coupling regime. In contrast to normal optomechanics, we focus on the nonlinear interaction between a parametric-amplification-squeezed ...