Laser cooling with electromagnetically induced transparency: application to trapped samples of ions or neutral atoms

A novel method of ground-state laser cooling of trapped atoms utilizes the absorption profile of a three- (or multi-) level system that is tailored by a quantum interference. With cooling rates comparable to conventional sideband cooling, lower final temperatures may be achieved. The method was experimentally implemented to cool a single Ca⁺ ion to its vibrational ground state. Since a broad band of vibrational frequencies can be cooled simultaneously, the technique will be particularly useful for the cooling of larger ion strings, thereby being of great practical importance for initializing a quantum register based on trapped ions. We also discuss its application to different level schemes and for ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field. Received: 10 July 2001 / Published online: 23 November 2001     

Scheme for direct measurement of the Wigner characteristic function of traveling fields

We present a proposal to measure field states for traveling modes. The scheme leads, in a simple and direct way, to the characteristic function of the state, yielding the determination of the Wigner function without a demanding data analysis. We employ a Mach-Zehnder interferometer including an auxiliary nonlinear medium in one arm. Analogies with other proposals to reconstruct states of stationary fields and trapped atoms are discussed.     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Experimental realization of deterministic entanglement transformations of bipartite pure states

We experimentally realize a kind of entanglement transformations of bipartite pure states with 100% efficiency. The protocol employs two-outcome positive operator-valued measures (POVMs) and can transform two-photon maximally entangled state to any two-photon entangled pure state with 100% efficiency. The average fidelity of all output states is 96%. Moreover, the scheme to implement arbitrary POVM on single-photon polarization state is also discussed. In principle, our setup can be applied to any kind of entanglement transformations of two-qubit entangled states to achieve optimal successful probability.     

Trapping State in a System of Single Three-level Trapped Ion Driven by External Fields

We investigate the interaction of a single three-level trapped ion with two laser beams. By applying a unitary transformation and a small rotating transformation, an exact solution to this quantum system is obtained without performing the Lamb-Dicke approximation, and the trapping state is observed.     

Preparation of Entanglement of Atoms and of Photons via Cavity Input-Output Process

We propose a method to prepare multipartite entangled states such as cluster states and graph states based on the cavity input-output process and single photon measurement. Two quantum gates, a controlled phase gate and a fusion gate between two atoms trapped in respective cavities, are proposed to prepare atomic cluster states and graph states with one and two dimensions. We also introduce a scheme that can generate an arbitrary multipartite photon duster state which uses two coherent states as a qubit basis.     

Ground state laser cooling using electromagnetically induced transparency

A laser cooling method for trapped atoms is described which achieves ground state cooling by exploiting quantum interference in a driven Lambda-shaped arrangement of atomic levels. The scheme is technically simpler than existing methods of sideband cooling, yet it can be significantly more efficient, in particular when several motional modes are involved, and it does not impose restrictions on the transition linewidth. We study the full quantum mechanical model of the cooling process for one motional degree of freedom and show that a rate equation provides a good approximation.     

Teleporting an Unknown Two-qubit Entangled State via Ion-Trap Systems

We propose a scheme for teleportation of an unknown two-qubit entangled state via trapped ions. In this scheme, we use the GHZ state as a quantum channel and the success probability can reach 1. The distinct advantage of our scheme is insensitive to the heating of the vibrational mode. In addition, Bell-state measurement is not required.     

Three-photon interference spectra in four-level atomic systems

We have considered the interference spectra that occur at the three-photon generated frequency arising from the interaction of three laser fields with a four-level atom, where two of the laser fields are on two-photon resonance with the three levels forming a “λ” scheme while the third laser operates between the second ground and the second excited state of the atom. At low intensities of all three laser fields, the overall intensity of the peak at the three-photon generated frequency, describing the spectrum of an electron in the second excited state, depends on the strength of the combined field of the two laser fields that are on two-photon resonance and it takes negative values. This indicates that light amplification without population inversion is likely to occur at the three-photon generated frequency. The combined field of the three laser fields induces multiphoton excitations near the three-photon generated frequency, whose peaks are characterized by linewidths which are much less than the natural linewidths of the atoms. These excitations describe absorption or stimulating emission processes depending on the values of the detunings of the laser fields. The derived results are graphically presented and discussed. Received: 24 January 2001 / Published online: 8 June 2001     

Quantum State Transfer in Trapped-Ion-Cavity Systems

We study the information transfer and entanglement transfer in a system consisting of single trapped ions in cavities by the three-mode cross-Kerr-like interaction among the cavity field （photons）, the centre-of-mass motion （phonons） and the internal state of the trapped ion in the Lamb-Dicke and large detuning regime.     

Sideband control of optical bistability and multistability

We present sideband control of optical bistability and multistability based on trichromatic electromagnetic-field induced transparency and quantum interference. Appearance or disappearance of the bistability and multistability, manipulation of the hysteresis loop widths, and switching between bistability and tristability are achieved simply by varying the sideband amplitudes or the relative phases of the sidebands to the central component.     

Entangled Radiation through an Atomic Reservoir Controlled by Coherent Population Trapping

We show that it is possible to generate Einstein-Podolsky-Rosen （EPR） entangled radiation using an atomic reservoir controlled by coherent population trapping. A beam of three-level atoms is initially prepared in nearcoherent population trapping （CPT） state and acts as a long-lived coherence-controlled reservoir. Four-wave mixing leads to amplification of cavity modes resonant with RabJ sidebands of the atomic dipole transitions. The cavity modes evolve Jnto an EPR state, whose degree of entanglement is controlled by the intensities and the frequencies of the driving fields. This scheme uses the long-lived CPT coherence and is robust against spontaneous emission of the atomic beam. At the same time, this scheme is implemented in a one-step procedure, not in a two-step procedure as was required in Phys. Rev. Lett. 98 （2007） 240401.     

Two-Time Intensity Correlations and Multiple Interference Mechanisms in a Driven Cascade Atom

We examine the intensity correlation functions of the two fluorescent fields that are emitted from the top and middle states of a doubly driven three-level atom in the cascade configuration. Novel interference effects are shown. （i） Both of the fluorescent fields have anticorrelations which can exist for long times when the applied fields are on the two-photon resonance and far off one.photon resonances. （ii） Both of the fluorescent fields have strong correlations when the applied fields are far off one- and two-photon resonances. In particular, the extremely strong correlation occurs for the photons emitted from the top state. The above phenomena are traced to the multiple interference mechanisms.     

Trapped-ion state detection through coherent motion

We demonstrate a general method for state detection of trapped ions that can be applied to a large class of atomic and molecular species. We couple a spectroscopy ion (27Al+) to a control ion (25Mg+) in the same trap and perform state detection through off-resonant laser excitation of the spectroscopy ion that induces coherent motion. The motional amplitude, dependent on the spectroscopy ion state, is measured either by time-resolved photon counting or by resolved sideband excitations on the control ion. The first method provides a simplified way to distinguish clock states in 27Al+, which avoids ground-state cooling and sideband transitions. The second method reduces spontaneous emission and optical pumping on the spectroscopy ion, which we demonstrate by nondestructively distinguishing Zeeman sublevels in the (1)S0 ground state of 27Al+.     

Two-photon spectral coherence matrix and characterization of multi-parameter entangled states

In this Letter we discuss how the classical coherence matrix can be generalized to describe the quantum properties of broadband two-photon entangled states. Procedures for experimental evaluation of two-photon matrix elements have been outlined. We illustrate how this formalism can be used for characterization of multi-parameter optical entanglement and discuss its possible applications in quantum optical measurement and quantum coherent control.     

Two-photon interaction between trapped ions and cavity fields

In this paper, we generalize the ordinary two-photon Jaynes-Cummings model (TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic well. A typical setup would be an optical cavity containing a single ion in a Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field coupling becomes highly nonlinear what brings out quite different behaviours for the system dynamics when compared to the ordinary TPJCM. In particular, we derive an effective two-photon Hamiltonian with dependence on the number operator of the ion's center-of-mass motion. This dependence occurs both in the cavity induced Stark-shifts and in the ion-field coupling, and its role in the dynamics is illustrated by showing the time evolution of the probability of occupation of the electronic levels for simple initial preparations of the state of the system.     

Two-photon revival-collapse phenomenon in the evolution of the quadrature squeezing of the four-photon Jaynes-Cummings model

We prove that the revival-collapse phenomenon occurring in the atomic inversion of the two-photon Jaynes-Cummings model, when the mode is initially prepared in the coherent state and the atom is in the excited state, can be obtained from the evolution of the quadrature squeezing of the four-photon Jaynes-Cummings model.     

Ground State of Jaynes-Cummings Model: Comparison of Solutions with and without the Rotating-Wave Approximation

The eigenenergy spectrum of the Jaynes-Cummings （JC） model with and without the rotating-wave approx- imation （RWA） is investigated. The numerical analysis indicates that the non-RWA spectrum can only be approximated by the RWA in the range of sufficiently small coupling constant and detuning. In other region, the counter-rotating terms remarkably change the nature of the RWA energy spectrum. A simple expression with high accuracy for ground eigenenergy and eigenvector non-RWA shows that the ground state is not a dark state state. for non-RWA is available. The ground eigenvector for and very different from that of RWA which is a dark state.     

Investigation of atomic coherence in multilevel systems with embedded tunable dark state superposition

The coherent superposition of two-atomic levels induced by coherent population trapping is employed in the two-level system, the standard three-level Λ type scheme and the four-level N-type systems and a weak probe pulse scans across the system. A theoretical analysis about the response of medium to the probe field is given. It is shown that under different initial conditions, the coherent superposition of the dark state exhibits abundant optical phenomena response to the probe field. It can change the absorption or gain and the dispersion relationship in the medium experienced by the probe. In the embedded three-level scheme, the probe experiences a crossover from absorption to transparent and then to amplification. Consequently the group velocity of the probe pulse can be controlled to propagate either as a subluminal, a standard, a superluminal or even a negative speed. In the embedded four-level N-type system, it can give an enhancement to the Giant Kerr effect and overcome the limitation of two-photon absorption, then make the nonlinear properties of the medium richer than the traditional N-type scheme.