Coupling of effective one-dimensional two-level atoms to squeezed light

A cavity QED system is analyzed which duplicates the dynamics of a two-level atom in free space interacting exclusively with broadband squeezed light. We consider atoms in a three or four-level Lambda-configuration coupled to a high-finesse optical cavity which is driven by a squeezed light field. Raman transitions are induced between a pair of stable atomic ground states via the squeezed cavity mode and coherent driving fields. An analysis of the reduced master equation for the atomic ground states shows that a three-level atomic system has insufficient parameter flexibility to act as an effective two-level atom interacting exclusively with a squeezed reservoir. However, the inclusion of a fourth atomic level, coupled dispersively to one of the two ground states by an auxiliary laser field, introduces an extra degree of freedom and enables the desired interaction to be realised. As a means of detecting the reduced quadrature decay rate of the effective two-level system, we examine the transmission spectrum of a weak coherent probe field incident upon the cavity

Multipartite Entanglement and Quantum State Exchange

We investigate multipartite entanglement in relation to the theoretical process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a novel measure called the entanglement of minimum bipartite entropy.Comment: 12 pages, 4 figure

Mimicking a Squeezed Bath Interaction: Quantum Reservoir Engineering with Atoms

The interaction of an atomic two-level system and a squeezed vacuum leads to interesting novel effects in atomic dynamics, including line narrowing in resonance fluorescence and absorption spectra, and a suppressed (enhanced) decay of the in-phase and out-of phase component of the atomic polarization. On the experimental side these predictions have so far eluded observation, essentially due to the difficulty of embedding atoms in a 4 pi squeezed vacuum. In this paper we show how to ``engineer'' a squeezed-bath-type interaction for an effective two-level system. In the simplest example, our two-level atom is represented by the two ground levels of an atom with angular momentum J=1/2 -> J=1/2 transition (a four level system) which is driven by (weak) laser fields and coupled to the vacuum reservoir of radiation modes. Interference between the spontaneous emission channels in optical pumping leads to a squeezed bath type coupling, and thus to symmetry breaking of decay on the Bloch sphere. With this system it should be possible to observe the effects predicted in the context of squeezed bath - atom interactions. The laser parameters allow one to choose properties of the squeezed bath interaction, such as the (effective) photon number expectation number N and the squeezing phase phi. We present results of a detailed analytical and numerical study.Comment: 24 pages, 8 figure

Entangled-State Cycles of Atomic Collective-Spin States

We study quantum trajectories of collective atomic spin states of $N$ effective two-level atoms driven with laser and cavity fields. We show that interesting ``entangled-state cycles'' arise probabilistically when the (Raman) transition rates between the two atomic levels are set equal. For odd (even) $N$, there are $(N+1)/2$ ($N/2$) possible cycles. During each cycle the $N$-qubit state switches, with each cavity photon emission, between the states $(|N/2,m>\pm |N/2,-m>)/\sqrt{2}$, where $|N/2,m>$ is a Dicke state in a rotated collective basis. The quantum number $m$ ($>0$), which distinguishes the particular cycle, is determined by the photon counting record and varies randomly from one trajectory to the next. For even $N$ it is also possible, under the same conditions, to prepare probabilistically (but in steady state) the Dicke state $|N/2,0>$, i.e., an $N$-qubit state with $N/2$ excitations, which is of particular interest in the context of multipartite entanglement.Comment: 10 pages, 9 figure

Motion-light parametric amplifier and entanglement distributor

We propose a scheme for entangling the motional mode of a trapped atom with a propagating light field via a cavity-mediated parametric interaction. We then show that if this light field is subsequently coupled to a second distant atom via a cavity-mediated linear-mixing interaction, it is possible to transfer the entanglement from the light beam to the motional mode of the second atom to create an EPR-type entangled state of the positions and momenta of two distantly-separated atoms.Comment: 9 pages, 8 figures, REVTe

Generation of two-mode nonclassical states and a quantum phase gate operation in trapped ion cavity QED

We propose a scheme to generate nonclassical states of a quantum system, which is composed of the one-dimensional trapped ion motion and a single cavity field mode. We show that two-mode SU(2) Schr\"odinger-cat states, entangled coherent states, two-mode squeezed vacuum states and their superposition can be generated. If the vibration mode and the cavity mode are used to represent separately a qubit, a quantum phase gate can be implemented.Comment: to appear in PR

Deterministic cavity quantum electrodynamics with trapped ions

We have employed radio-frequency trapping to localize a single 40Ca+-ion in a high-finesse optical cavity. By means of laser Doppler cooling, the position spread of the ion's wavefunction along the cavity axis was reduced to 42 nm, a fraction of the resonance wavelength of ionized calcium (λ = 397 nm). By controlling the position of the ion in the optical field, continuous and completely deterministic coupling of ion and field was realized. The precise three-dimensional location of the ion in the cavity was measured by observing the fluorescent light emitted upon excitation in the cavity field. The single-ion system is ideally suited to implement cavity quantum electrodynamics under cw conditions. To this end we operate the cavity on the D3/2–P1/2 transition of 40Ca+ (λ = 866 nm). Applications include the controlled generation of single-photon pulses with high efficiency and two-ion quantum gates

Analysis of dynamical tunnelling experiments with a Bose-Einstein condensate

Dynamical tunnelling is a quantum phenomenon where a classically forbidden process occurs, that is prohibited not by energy but by another constant of motion. The phenomenon of dynamical tunnelling has been recently observed in a sodium Bose-Einstein condensate. We present a detailed analysis of these experiments using numerical solutions of the three dimensional Gross-Pitaevskii equation and the corresponding Floquet theory. We explore the parameter dependency of the tunnelling oscillations and we move the quantum system towards the classical limit in the experimentally accessible regime.Comment: accepted for publication in Physical Review

Dissipation-driven quantum phase transitions in collective spin systems

We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions can occur as the dissipation strength is varied. First, we consider a well known model of cooperative resonance fluorescence that can exhibit a second-order quantum phase transition, and analyze the entanglement properties near the critical point. Next, we examine a dissipative version of the Lipkin-Meshkov-Glick interacting collective spin model, where we find that either first- or second-order quantum phase transitions can occur, depending only on the ratio of the interaction and external field parameters. We give detailed results and interpretation for the steady state entanglement in the vicinity of the critical point, where it reaches a maximum. For the first-order transition we find that the semiclassical steady states exhibit a region of bistability.Comment: 12 pages, 16 figures, removed section on homodyne spectr

Thermal Properties of Interacting Bose Fields and Imaginary-Time Stochastic Differential Equations

Matsubara Green's functions for interacting bosons are expressed as classical statistical averages corresponding to a linear imaginary-time stochastic differential equation. This makes direct numerical simulations applicable to the study of equilibrium quantum properties of bosons in the non-perturbative regime. To verify our results we discuss an oscillator with quartic anharmonicity as a prototype model for an interacting Bose gas. An analytic expression for the characteristic function in a thermal state is derived and a Higgs-type phase transition discussed, which occurs when the oscillator frequency becomes negative.Comment: Published versio