Dicke Limit Research Articles

Lamb–Dicke localization of cold atoms in Ferris wheel optical dipole potential

We investigate the possibility of strong localization, of the Lamb–Dicke type, for cold atoms trapped by a far off-resonant Ferris wheel optical dipole potential. This optical dipole potential light field is created when a light field generated by the superposition of two similar co-propagating Laguerre–Gaussian beams, with opposite winding numbers, interacts with a two-level atom. We show that strong confinement of atoms in such a light field is possible when the light field is tightly focused, for low values of the winding number and relatively high values of power. We show that a combination of a Ferris wheel with an ordinary axial Gaussian optical lattice provides 3D cylindrically symmetric optical lattices in which the Lamb–Dicke limit can be reached for typically used experimental parameter values.

NOON state generation beyond the Lamb–Dicke limit in trapped-ion systems

In this paper, we show that multi-phonon NOON states can be generated in a two-dimensional anisotropic trapped-ion system. In the proposal, two laser pulses are applied to an ion along different directions in the ion trap plane to exchange the information between the external and internal states of the ion. Different from the previous frameworks, the proposal is outside the Lamb–Dicke regime. The distinct advantage of the proposed scheme is that the entanglement generation is deterministic and no measurement on the system is required. Numerical simulations show that the fidelity of the prepared entangled states is strongly affected by Lamb–Dicke parameters.

Symmetry-protected single-photon subradiance

We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that anti-symmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.

Gamma-ray laser based on the collective decay of positronium atoms in a Bose-Einstein condensate

We consider, in general, the collective two-photon annihilation decay of positronium atoms arising from the second quantized formalism. It is shown that two-photon annihilation of positronium atoms in a Bose-Einstein condensate (BEC) is unstable. Due to the BEC coherence, an absolute instability in such system takes place, i.e., the number of photons created as a result of positronium decay grows in every point within a BEC. The latter leads to an exponential buildup of a macroscopic population into the certain modes. Cooperative effects start for densities much smaller than the Dicke limit of spontaneous super radiation. For laserlike action, i.e., for directional radiation, we consider the BEC with elongated shape when the spontaneously emitted entangled and oppositely directed photon pairs are amplified, leading to an exponential buildup of a macroscopic population into the end-fire modes. We also consider the roles of confinement and interaction among positronium atoms in the amplification process.

Full-trapped three-level ion in the lamb–dicke limit: analyzing and comparing quantum entanglement measures of two qudits

Our aim is to investigate the entanglement dynamics and quantum correlations of a full-trapped ion interacting with two time-independent laser beams in view of the Lamb–Dicke parameter. For this purpose, the three probability amplitudes in the trapped ion is taken as $ \sqrt {{{{1} \left/ {3} \right.}}} $ . Concurrence, negativity, and atomic Wehrl entropy of entanglement exhibit a long interacting time. We show that long survival is proved with these quantum measures.

Entanglement between internal and external degrees of freedom of a driven trapped atom

We study the dynamics of a Λ-shaped trapped atom that is driven by two lasers to conditions approaching electromagnetically induced transparency. Solving numerically the full quantum master equation describing the coupled system of electronic and vibrational degrees of freedom, we investigate the dynamics of the entanglement and the quantum mutual information during the cooling process. Far from the Lamb–Dicke limit, an intricate behaviour of these quantities is found, as well as the emergence of a mixed entangled non-equilibrium stationary state.

Controlled-NOT gate for manipulating photonic polarization states in a two-mode optical cavity

We investigate the coherent interaction between two cavity modes with left or right circular polarizations and a traveling atom in the four-level Y configuration. With large single-photon detunings for both cavity modes and in the presence of a strong classical field, all one-photon and two-photon transitions may be well eliminated so that a close-loop four-photon transition starting from the only populated ground state becomes absolutely dominant. This physical scenario is then exploited to devise an efficient controlled-NOT gate for manipulating polarization states of two intracavity photons. In the Lamb–Dicke limit and in the strong coupling regime, the expected controlled-NOT operation is found to have a rather high gate fidelity and a moderate photon loss.

Generation of four-atom entangled decoherence-free states by interference of polarized photons

We propose a protocol to generate four-atom entangled decoherence-free states trapped in distant cavities by using the interference of polarized photons. The protocol uses the effects of quantum statistics of indistinguishable photons emitted by the atoms inside optical cavities. In the Lamb–Dicke limit, the protocol does not require the simultaneous click of detectors. This makes the protocol more realizable in experiments.

Arbitrary state controlled-unitary gate between two remote atomic qubits via adiabatic passage

We generalize the scheme of Lacour et al. [X. Lacour, N. Sangouard, S. Guerin, H.R. Jauslin, Phys. Rev. A 73 (2006) 042321] to the case of nonlocal qubits, which makes the resultant gate suitable for distributed quantum computation. In our scheme, two remote atomic qubits are separately trapped in two distant cavities connected by an optical fiber. Based on adiabatic passage, our scheme is immune to the decoherence due to spontaneous emission and to photon decay from the cavity modes and the fiber mode. Moreover, our scheme can work robustly beyond the Lamb–Dicke limit. It is shown that the minimum fidelity of the resultant gate operation for an arbitrary input state could be over 0.98.

Collective Lamb Shift in Single Photon Dicke Superradiance

The collective Lamb shift and associated radiative decay of a large cloud of radius R containing N atoms uniformly excited by one photon of wavelength lambda is analyzed. It is shown that the time evolution of the symmetric state prepared by single photon absorption in the limit R>>lambda is similar to that encountered in the Dicke limit of small sample (R<<lambda) superradiance. The theory includes virtual (counterrotating) terms naturally and thus provides a simple calculation of the collective Lamb shift of a single Dicke state.

A simple Scheme for Generating an n-Qubit W State in a Trapped-Ion System without a Lamb–Dicke Limit

A simple and scalable scheme is proposed to generate a n-qubit W state in a trapped-ion system without the Lamb–Dicke limit. The n-qubit W state can be generated by the interaction between the ions and the laser field if the collective mode is initially prepared in the single-phonon state and each ion is in the ground state. The scheme only requires a single laser and avoids laser manipulation of the individual ion. The time required to complete the process decreases with the number of ions. The present scheme is not limited to small values of the LD parameter, which greatly enhances operation speeds.

Quantum logic gates with two-level trapped ions beyond Lamb–Dicke limit

In the system with two two-level ions confined in a linear trap, this paper presents a simple scheme to realize the quantum phase gate (QPG) and the swap gate beyond the Lamb–Dicke (LD) limit. These two-qubit quantum logic gates only involve the internal states of two trapped ions. The scheme does not use the vibrational mode as the data bus and only requires a single resonant interaction of the ions with the lasers. Neither the LD approximation nor the auxiliary atomic level is needed in the proposed scheme. Thus the scheme is simple and the interaction time is very short, which is important in view of decoherence. The experimental feasibility for achieving this scheme is also discussed.

Long-lived entangled qudits in a trapped three-level ion beyond the Lamb–Dicke limit

Higher dimensional quantum entanglement in a trapped three-level ion interacting with two laser beams in Λ scheme is investigated beyond the Lamb–Dicke limit. It is shown that higher dimensional entanglement can be established in a single step, with a tunable dimensionality and duration via the Lamb–Dicke parameter.

Super- and subradiant emission of two-level systems in the near-Dicke limit

We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the system are studied using a renormalized master equation, both with multipolar and minimal-coupling interaction schemes. We show that both models lead to the same result and, in contrast to nonrenormalized models, predict that the relative orientation of the (coaligned) dipoles is unimportant in the Dicke limit. Our master equation is of relevance to any system of dipole-coupled two-level atoms, and gives bounds on the strength of the dipole-dipole interaction for closely spaced atoms. Exact calculations for small atom systems in the near-Dicke limit show the increased emission times resulting from the evolution generated by the strong dipole-dipole interaction. However, for large numbers of atoms in the near-Dicke limit, it is shown that as the number of atoms increases, the effect of the dipole-dipole interaction on collective emission is reduced.

Generation of squeezed quantum states of a single trapped cold ion

Based on the quantum dynamics of laser-ion interaction beyond the Lamd_Dicke limit, we discuss how to superpose a series of vibrational number states of a single trapped ion from the motional ground state. It is shown that, by controlling the durations and phases of the sequentially applied laser pulses, these superposed quantum states could well approach to the various target quantum states, e.g., squeezed coherent states, squeezed odd/even coherent states and squeezed vacuum states, etc.Their experimental realizabilities are also discussed.

Scheme for reliable realization of quantum logic gates for two atoms separately trapped in two distant cavities via optical fibers

An approach for realizing conditional phase gate for two atoms separately trapped in two distant cavities mediated by an optical fiber is proposed. Utilizing the adiabatic passage, the atomic spontaneous emission, and the decays of the fiber and cavities are avoided under certain condition. The effects of the losses in the fiber and cavities on the fidelity are analyzed. Moreover, our scheme is not restricted to Lamb–Dicke limit. We also generalize the approach to generate one-dimensional cluster state and entangled state for two collections of atoms.

Squeezing properties of a trapped ion in the running-wave laser beyond the Lamb–Dicke limit

Beyond the Lamb–Dicke limit, this paper investigates the squeezing properties of the trapped ion in the travelling-wave laser. It shows that the squeezing properties of the trapped ion in the travelling-wave laser are strongly affected by the sideband number k, the Lamb–Dicke parameter η and the initial average phonon number.

A scheme of quantum phase gate for trapped ion

We propose a scheme to implement two-qubit controlled quantum phase gate(CQPG) via a single trapped two-level ion located in the standing wave field of a quantum cavity, in which the trap works beyond the Lamb–Dicke limit. When the light field is resonant with the atomic transition |g> ↔ |e> of the ion located at the antinode of the standing wave, we can perform CQPG between the internal and external states of the trapped ion; while the frequency of the light field is chosen to be resonant with the first red sideband of the collective vibrational mode of the ion located at the node of the standing wave, we can perform CQPG between the cavity mode and the collective vibrational mode of the trapped ion. Neither the Lamb–Dicke approximation nor the assistant classical laser is needed. Also we can generate a GHZ state if assisted with a classical laser.

Lower ground state due to counter-rotating wave interaction in a trapped ion system

We consider a single ion confined in a trap under the radiation of two travelling waves of lasers. In the strong-excitation regime and without the restriction of the Lamb–Dicke limit, the Hamiltonian of the system is similar to a driving Jaynes–Cummings model without the rotating wave approximation (RWA). The approach we developed enables us to present complete eigensolutions, which makes it possible to compare with the solutions under the RWA. We find that the ground state in our non-RWA solution is energetically lower than the counterpart under the RWA. If we have the ion in the ground state, it is equivalent to a spin dependent force on the trapped ion. Discussion is given for the difference between the solutions with and without the RWA, and for the relevant experimental test, as well as for the possible application to quantum information processing.

Decoherence-free quantum-information processing using dipole-coupled qubits

We propose a quantum-information processor that consists of decoherence-free logical qubits encoded into arrays of dipole-coupled qubits. High-fidelity single-qubit operations are performed deterministically within a decoherence-free subsystem without leakage via global addressing of bichromatic laser fields. Two-qubit operations are realized locally with four physical qubits, and between separated logical qubits using linear optics. We show how to prepare cluster states using this method. We include all non-nearest-neighbor effects in our calculations, and we assume the qubits are not located in the Dicke limit. Although our proposal is general to any system of dipole-coupled qubits, throughout the paper we use nitrogen-vacancy (NV) centers in diamond as an experimental context for our theoretical results.