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...