We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical micro-cavity. Single atom strongly couples to the high-order transverse vacuum TEM_{10} mode, instead of the usual TEM_{00} mode, and the parameter of the system is (g_{10},κ,γ)=2π\times (20.5,2.6,2.6)MHz. The atoms simply fall down freely from the magneto-optic trap into the cavity modes and the trajectories of the single atoms are linear. The transmission spectrums of atoms passing through the TEM10 mode are detected by a single photon counting modules and well fitted. Thanks to the tilted cavity transverse TEM10 mode, which is inclined to the vertical direction about 45 degrees and it helps us, for the first time, to eliminate the degenerate trajectory of the single atom falling through the cavity and get the unique atom trajectory. Atom position with high precision of 0.1μm in the off-axis direction (axis y) is obtained, and the spatial resolution of 5.6μm is achieved in time of 10μs along the vertical direction (axis x). The average velocity of the atoms is also measured from the atom transits, which determines the temperature of the atoms in magneto-optic trap, 186μK {\pm} 19μK.
We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom. The atom may tunnel between sites in the lattice. We find the photon counting statistic $g^{(2)}(τ)$ depends on the tunneling rate. Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation, in ther Josephson junction regime. It is shown that oscillations in $g^{(2)}(τ)$ are directly proportional to the tunneling coefficient. We work in the bad-cavity limit a…
We generalize the Power-Zineau-Woolley transformation to obtain a canonical Hamiltonian of cavity quantum electrodynamics for arbitrary geometry of boundaries. This Hamiltonian is free from the A-square term and the instantaneous Coulomb interaction between distinct atoms. The single-mode models of cavity QED (Dicke, Tavis-Cummings, Jaynes-Cummings) are justified by a term by term mapping to the proposed microscopic Hamiltonian. As one straightforward consequence, the basis of no-go argumentations concerning the Dicke phase transition with atoms in electromagnetic fields dissolves.
We consider an ensemble of cavity-coupled two-level emitters interacting via full (coherent and dissipative) dipole-dipole interactions. Using an adiabatic elimination procedure we derive effective equations of motion for a subsystem consisting of the cavity and a single emitter. Those equations can be used for schemes to enhance the cavity-coupling of single emitters as shown in [S. Schütz, J. Schachenmayer, D. Hagenmüller, G. K. Brennen, T. Volz, V. Sandoghdar, T. W. Ebbesen, C. Genes, and G. Pupillo, e-print arXiv:1904.08888]. We analyze limitations of effective subsystem parameters, and st…
Thermal noise of a mirror is one of the most important issues in high precision measurements such as gravitational-wave detection or cold damping experiments. It has been pointed out that thermal noise of a mirror with multi-layer coatings can be reduced by mechanical separation of the layers. In this paper, we introduce a way to further reduce thermal noise by locking the mechanically separated mirrors. The reduction is limited by the standard quantum limit of control noise, but it can be overcome with a quantum-non-demolition technique, which finally raises a possibility of complete eliminat…
We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation trea…
Effective Hamiltonians in Cavity and Waveguide QED from Transition-Operator Diagrammatic Perturbation Theory
Telecom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎理工学院）；Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 6303 CNRS - Université de Bourgogne Franche-Comté（勃艮第卡诺跨学科实验室，CNRS联合研究单位6303，勃艮第弗朗什-孔泰大学）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学，自然科学学院，物理系）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Centre for Nanosciences and Nanotechnology, Université Paris-Saclay（纳米科学与工程中心，巴黎萨克雷大学）
We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination technique to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We investigate the many body steady states and the self-organization transition for a wide range of parameters. We show that in the self-organized phase the steady state consi…
Tracing the dynamics of a quantum system using a mesoscopic device is an important topic of interest nowadays. Here we show how a mesoscopic mechanical oscillator steers the dynamics of a coupled two-atom system and gives rise to a two-qubit SWAP gate. We have theoretically studied a generic hybrid atom-optomechanical system where two identical atoms in $Λ$ configuration are trapped inside the cavity and the cavity mode mediates the interaction between the atoms and the mechanical oscillator. Adiabatic elimination of the lossy channels is adopted which in turn gives rise to an effective Hamilt…
We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of back-action noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broad-band detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise cancels exa…
Cavity cooling via quantum backaction force can extract thermal fluctuations from a mechanical resonator to reach the quantum ground state. Surface or bulk two-level-system (TLS) defects in a mechanical resonator can couple with the mechanical mode via deformation potential and affect the cooling process significantly. Here, we develop a theory to study the cavity cooling of a mechanical mode in the presence of a TLS defect using the adiabatic elimination technique. Our result shows that the cooling process depends strongly on the resonance and the damping rate of the TLS.
We investigate how to describe the dissipative spin dynamics of the driven-dissipative Dicke model, describing $N$ two-level atoms coupled to a cavity mode, after adiabatic elimination of the cavity mode. To this end, we derive a Redfield master equation which goes beyond the standard secular approximation and large detuning limits. We show that the secular (or rotating wave) approximation and the large detuning approximation both lead to inadequate master equations, that fail to predict the Dicke transition or the damping rates of the atomic dynamics. In contrast, the full Redfield theory cor…
We study theoretically the interaction between two photons in a nonlinear cavity. The photons are loaded into the cavity via a method we propose here, in which the input/output coupling of the cavity is effectively controlled via a tunable coupling to a second cavity mode that is itself strongly output-coupled. Incoming photon wave packets can be loaded into the cavity with high fidelity when the timescale of the control is smaller than the duration of the wave packets. Dynamically coupled cavities can be used to avoid limitations in the photon-photon interaction time set by the delay-bandwidt…
We theoretically analyze antibunching of the phonon field in an optomechanical oscillator employ- ing the membrane-in-the-middle geometry. More specifically, a single-mode mechanical oscillator is quadratically coupled to a single-mode cavity field in the regime in which the cavity dissipation is a dominant source of damping, and adiabatic elimination of the cavity field leads to an effective cubic nonlinearity for the mechanics. We show analytically in the weak coupling regime that the mechan- ics displays a chaotic phonon field for small optomechanical cooperativity, whereas an antibunched s…
In dissipative quantum systems, strong symmetries can lead to the existence of conservation laws and multiple steady states. In this work we investigate a strong symmetry for bosonic atoms coupled to an optical cavity, an experimentally relevant system, generalizing the adiabatic elimination techniques and using numerically exact matrix product state methods. We show that for ideal bosons coupled to the cavity multiple steady states exist and in each symmetry sector a dissipative phase transition occurs at a different critical point. This implies that phases of very different nature can coexis…
We analyze the optomechanics of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a uniform bias force such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice at the Bloch frequency. When the Bloch frequency is on the order of the cavity damping rate we find transport of the atoms either up or down the lattice. The transport dynamics can be interpreted as a manifestation of…
Despite the enormous technological interest in micro and nanolasers, surprisingly, no class-B quantum density-matrix model is available to date, capable of accurately describing coherence and photon correlations within a unified theory. In class-B lasers $-$applicable for most solid-state lasers at room temperature$-$, the macroscopic polarization decay rate is larger than the cavity damping rate which, in turn, exceeds the upper level population decay rate. Here we carry out a density-matrix theoretical approach for generic class-B lasers, and provide closed equations for the photonic and ato…
We present two approaches capable of describing the dynamics of an interacting many body system on a lattice coupled globally to a dissipative bosonic mode. Physical realizations are for example ultracold atom gases in optical lattice coupled to a photonic mode of an optical cavity or electronic gases in solids coupled to THz cavity fields. The first approach, applicable for large dissipation strengths and any system size, is a variant of the many-body adiabatic elimination method for investigating the long time dynamics of the system. The second method extends the time-dependent matrix produc…
We predict a bistability in the photon emission from a solid-state single-atom laser comprising a microwave cavity coupled to a voltage-biased double quantum dot. To demonstrate that the single-atom laser is bistable, we evaluate the photon emission statistics and show that the distribution takes the shape of a tilted ellipse. The switching rates of the bistability can be extracted from the electrical current and the shot noise in the quantum dots. This provides a means to control the photon emission statistics by modulating the electronic transport in the quantum dots. Our prediction is robus…
We calculate the steady-state and first-order time varying atom-field correlation functions in the weak-excitation limit of absorptive optical bistability from a linearized theory of quantum fluctuations. We formulate a Fokker-Planck equation in the positive P representation following the phase-space analysis of [H. J. Carmichael, Phys. Rev. A 33, 3262 (1986)] which is suitable for the determination of cross-correlations as it does not resort to adiabatic elimination. Special emphasis is placed on the limit of collective strong coupling as attained from a vanishing photon-loss rate. We compare…
In this paper, we present a model which exhibits two identical $Ξ$-type three-level atoms interacting with a single-mode field with $k$-photon transition in an optical cavity enclosed by a Kerr medium. Considering full nonlinear formalism, it is assumed that the single-mode field, atom-field coupling and Kerr medium are all $f$-deformed. By using the adiabatic elimination method, it is shown that, the Hamiltonian of the considered system can be reduced to an effective Hamiltonian with two two-level atoms and $f$-deformed Stark shift. In spite of the fact that, the system seems to be complicate…
