Zbigniew Ficek

Entangled states and collective nonclassical effects in two-atom systems

We propose a review of recent developments on entanglement and nonclassical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

Delayed sudden birth of entanglement

The concept of time delayed creation of entanglement by the dissipative process of spontaneous emission is investigated. A threshold effect for the creation of entanglement is found where the initially unentangled qubits can be entangled after a finite time despite the fact that the coherence between the qubits exists for all times. This delayed creation of entanglement, which we call sudden birth of entanglement, is opposite to the currently extensively discussed sudden death of entanglement and is characteristic for transient dynamics of one-photon entangled states of the system. We determine the threshold time for the creation of entanglement and find it is related to time at which the antisymmetric state remains the only excited state being populated. It is shown that the threshold time can be controlled by the distance between the qubits and the direction of initial excitation relative to the interatomic axis. This effect suggests an alternative for the study of entanglement and provides an interesting resource for creation on demand of entanglement between two qubits.

Atoms in squeezed light fields

Squeezed light is of interest as an example of a non-classical state of the electromagnetic field and because of its applications both in technology and in fundamental quantum physics. This review concentrates on one aspect of squeezed light, namely its application in atomic spectroscopy. The general properties, detection and application of squeezed light are first reviewed. The basic features of the main theoretical methods (master equations, quantum Langevin equations, coupled systems) used to treat squeezed light spectroscopy are then outlined. The physics of squeezed light interactions with atomic systems is dealt with first for the simpler case of two-level atoms and then for the more complex situation of multi-level atoms and multi-atom systems. Finally the specific applications of squeezed light spectroscopy are reviewed.

Entanglement evolution of two remote and non-identical Jaynes–Cummings atoms

A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.

Generation of pure continuous-variable entangled cluster states of four separate atomic ensembles in a ring cavity

A practical scheme is proposed for the creation of continuous-variable entangled cluster states of four distinct atomic ensembles located inside a high-finesse ring cavity. The scheme does not require a set of external input squeezed fields, a network of beam splitters, and measurements. It is based on nothing else than the dispersive interaction between the atomic ensembles and the cavity mode and a sequential application of laser pulses of a suitably adjusted amplitudes and phases. We show that the sequential laser pulses drive the atomic “field modes” into pure squeezed vacuum states. The state is then examined against the requirement to belong to the class of cluster states. We illustrate the method on three examples of the entangled cluster states: the so-called continuous-variable linear, square, and T-type cluster states.

Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system

We study multipartite entanglement, the generation of Einstein-Podolsky-Rosen (EPR) states, and quantum steering in a three-mode optomechanical system composed of an atomic ensemble located inside a single-mode cavity with a movable mirror. The cavity mode is driven by a short laser pulse, has a nonlinear parametric-type interaction with the mirror and a linear beam-splitter-type interaction with the atomic ensemble. There is no direct interaction of the mirror with the atomic ensemble. A threshold effect for the dynamics of the system is found, above which the system works as an amplifier and below which as an attenuator of the output fields. The threshold is determined by the ratio of the coupling strengths of the cavity mode to the mirror and to the atomic ensemble. It is shown that above the threshold, the system effectively behaves as a two-mode system in which a perfect bipartite EPR state can be generated, while it is impossible below the threshold. Furthermore, a fully inseparable tripartite entanglement and even further a genuine tripartite entanglement can be produced above and below the threshold. In addition, we consider quantum steering and examine the monogamy relations that quantify the amount of bipartite steering that can be shared between different modes. It is found that the mirror is more capable for steering of entanglement than the cavity mode. The two-way steering is found between the mirror and the atomic ensemble despite the fact that they are not directly coupled to each other, while it is impossible between the output of cavity mode and the ensemble which are directly coupled to each other.

Gain without population inversion in a two-level atom damped by a broadband squeezed vacuum

We study the absorption spectrum of a two-level atom driven by a resonant laser field and damped by a broadband squeezed vacuum. We show that for some values of the Rabi frequency of the driving field the central component of the absorption spectrum can switch from absorption to amplification. We find that the presence of the squeezed vacuum field is essential for the gain at the central component. Moreover, the gain is not attributed to any population inversion in both the atomic bare states and in the dressed atomic states. We show that the gain originates from the coherent population oscillations, which are significantly enhanced when the atom is damped by a broadband squeezed vacuum.

Squeezing-induced transparency in a two-level atom

The effect of an off-resonance squeezed field on the weak probe-beam absorption spectrum of a two-level atom is discussed. A threshold effect for the squeezing is found, below which the spectrum consists of an absorptive and an emissive doublet of the same width and above which the spectra consists of two partly absorptive, partly dispersive features of different widths and both centered on the squeezing frequency. It is shown that below threshold a spectral hole may appear at the probe-beam frequency separated from the atomic transition frequency by twice the detuning of the squeezed field centre frequency from atom resonance. For a minimum uncertainty squeezed field of high intensity the probe absorption can be totally suppressed at this frequency and the system is transparent for the probe beam. These effects suggest new alternatives for the experimental study of the interaction of atoms with squeezed light. Described is a possible technique for testing these predictions, using a microscopic Fabry-Perot cavity.

Entanglement created by spontaneously generated coherence

We propose a scheme that is able to generate on demand a steady-state entanglement between two nondegenerate cavity modes. The scheme relies on the interaction of the cavity modes with driven two- or three-level atoms, which act as a coupler to build entanglement between the modes. We show that, in the limit of a strong driving, it is crucial for the generation of entanglement between the modes to imbalance populations of the dressed states of the driven atomic transition. In the case of a three-level V-type atom, we find that a stationary entanglement can be created on demand by tuning the Rabi frequency of the driving field to the difference between the atomic transition frequencies. The resulting degeneracy of the energy levels, together with the spontaneously generated coherence, generate a steady-state entanglement between the cavity modes. It is shown that the condition for the maximal entanglement coincides with the collapse of the atomic system into a pure trapping state. We also show that the creation of entanglement depends strongly on the mutual polarization of the transition atomic dipole moments.

Quantum beats and superradiant effects in the spontaneous emission from two nonidentical atoms

The problem considered is that of the spontaneous emission from two nonidentical two-level atoms coupled to a continuum of quantized electromagnetic modes. The atoms are separated by distances comparable to the resonant wavelength and have different transition frequencies and natural linewidths. Correlation functions and radiation rates are expressed in terms of expectation values of time-dependent atomic operators. The radiation pattern, total radiation rate and spectral distribution of radiation are obtained with the initial conditions that only one atom is excited and that the system is fully inverted. We find that the radiation pattern and total radiation rate show quantum beats when initially only one atom is excited. Moreover, the total radiation rate for strong interatomic interaction becomes greater than its initial value at the beginning of the emission process. This “superradiant” property is absent for two identical atoms. For initially fully inverted system, the radiation pattern and total radiation rate decay monotonically in time. Some weak beats can appear for drastically different atoms. The spectrum of radiation calculated for the case of strong interatomic interaction, i.e., for separations much smaller than the resonant wavelength shows two peaks, located at frequency ±Ω12, contrary to the case of identical atoms, when the spectrum consists of only one peak located at the frequency +Ω12.