Ensemble Of Two-level Atoms Research Articles

Quadripartite cluster and Greenberger–Horne–Zeilinger entangled light via cascade interactions with separated atomic ensembles

It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The responsible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here, we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nondegenerate fields. It is shown that the quadripartite cluster and Greenberger–Horne–Zeilinger entangled states occur for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance-based parametric processes.

The Purcell-Dicke effect in the emission from a coated small sphere of resonant atoms placed inside a matrix cavity

I investigate a system where both the Purcell effect and Dicke’s superradiance are present. I compute the frequency eigenmode for an ensemble of identical two-level atoms enclosed in a coated nanosphere that is embedded in a matrix. I show that, in a number of configurations, the rate of superradiant emission from the atomic system can be increased many folds from that of a similar cloud of atoms in free space.

Photon Production from the Vacuum Close to the Superradiant Transition: Linking the Dynamical Casimir Effect to the Kibble-Zurek Mechanism

The dynamical Casimir effect (DCE) predicts the generation of photons from the vacuum due to the parametric amplification of the quantum fluctuations of an electromagnetic field. The verification of such an effect is still elusive in optical systems due to the very demanding requirements of its experimental implementation. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way to an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of the DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.

Using quantum coherence to generate gain in the XUV and X-ray: gain-swept superradiance and lasing without inversion

It was shown some time ago that when the excitation of an ensemble of two-level atoms is swept in the direction of lasing, so that atoms are prepared in the excited state just as the radiation from previously excited atoms reaches them, the resulting laser amplifier is “highly anomalous” and yields superradiant emission without population inversion. We here show that transient gain in a three-level system has common features with Dicke superradiance and can yield strong extreme ultraviolet lasing in, for example, He atoms (at 58 nm) or He-like ions such as <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3+</sup> (at 6.1 nm).

Sideband entanglement in collective resonance fluorescence

We examine the quantum correlation between the Mollow sidebands in the collective resonance fluorescence from a strongly driven ensemble of two-level atoms. By using the criterion proposed by Shchukin and Vogel, we show that non-Gaussian entanglement exists between the two separated sidebands. The responsible mechanism is traced to the spontaneous parametric process, in which the nonclassical correlation is established. This suggests that the collective resonance fluorescence provides a continuous source for the non-Gaussian entangled light and thus has great potentials for various applications in quantum information and quantum computation.

Doppler cooling with coherent trains of laser pulses and a tunable velocity comb

We explore the possibility of decelerating and Doppler cooling of an ensemble of two-level atoms by a coherent train of short, non-overlapping laser pulses. We develop a simple analytical model for dynamics of a two-level system driven by the resulting frequency comb field. We find that the effective scattering force mimics the underlying frequency comb structure. The force pattern depends strongly on the ratio of the atomic lifetime to the repetition time and pulse area. For example, in the limit of short lifetimes, the frequency peaks of the optical force wash out. We show that laser cooling with pulse trains results in a "velocity comb", a series of narrow peaks in the velocity space.

Cavity cooling using intense blue-detuned light

We investigate the possibility of cooling an atomic gas enclosed in an optical cavity using blue-detuned laser light of sufficient intensity that excitation of the atoms cannot be neglected. We consider an ensemble of two-level atoms confined inside a simple Fabry–Perot cavity in two different geometric configurations: in one (‘cavity-pump’ configuration) the pump field is directed along the cavity axis and in the other (‘atom-pump’ configuration) the pump field is directed perpendicular to the cavity axis. Numerical simulations of the semi-classical models for each configuration are compared. Both configurations demonstrate cooling using a blue-detuned pump field. It is shown that in the cavity-pump configuration there is no collective enhancement of the cooling rate over that of free space blue-cooling. In contrast, the atom-pump configuration demonstrates collective enhancement of the cooling rate and intracavity field intensity.

High-temperature phase transition in the coupled atom-light system in the presence of optical collisions

The problem of photonic phase transition for the system of a two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OC) is considered. We have shown that for large and negative atom-field detuning a photonic field exhibits high temperature second order phase transition to superradiant state under thermalization condition for coupled atom-light states. Such a transition can be connected with superfluid (coherent) properties of photon-like low branch (LB) polaritons. We discuss the application of metallic cylindrical waveguide for observing predicted effects.

Quantum equations of motion for multimode laser generation with a spatial dependence of the atom interaction with the field taken into account

We derive equations of motion for the electromagnetic field operators a + aq for a three-level multimode laser with a spatial dependence of the interaction of atoms with the field of a standing wave in a cavity taken into account. We calculate and analyze the dynamics of means of photon numbers in the field modes and of the correlation function of field modes. We explore the effect of intermode correlations on the dynamics of establishing stationary laser generation. We find that taking the spatial dependence of the interaction of atoms with the field and the intermode correlation into account in investigating the means of photon numbers leads to revealing new properties of laser generation, such as saturation of the laser radiation intensity in a single-mode regime and generation of short light pulses of side below-threshold modes with the amplitudes depending on the initial state of the field in a cavity. Under the condition that the width of a laser amplification line (the rate of damping of the active medium polarization) is of the order of or greater than the intermode gap of eigenfrequencies in a cavity, laser generation has a multimode (multifrequency) nature. In real conditions, a small increase above the generation threshold, when the pumping is relatively small, can already lead to excitation of several eigen- modes of the laser cavity. With an increase in pumping, the number of modes involved in the generation and having intensities comparable to each other rapidly increases and can attain large values (up to sev- eral hundreds). The complicated dynamics of the multimode generation of different lasers are currently widely investigated both theoretically and experimentally. The theoretical analysis of multimode genera- tion encounters major complications because we must take intermode interactions into account, together with the spatial dependence of the interaction of the active medium atoms with a spatially inhomogeneous electromagnetic (EM) field in the cavity, which shows up, in particular, in the effect of spatial burning of a hole. The semiclassical theory of multimode (multifrequency) laser generation was developed in (1)-(10), where the Maxwell equations for a classical EM field were considered and the active medium was described quantum-mechanically in terms of a density matrix (operator) and an ensemble of two-level atoms. A full quantum mechanical theory of multimode generation was considered in (1), (11)-(16). The approximation of identical modes was used in (12)-(16). We note that in (1)-(4) in the semiclassical theory, the phenomenon of spatial burning of a hole in the population inversion of an active medium was regarded as the main reason and the necessary condition for the occurrence of stable multimode laser generation with a homogeneously broadened line. The approximation of identical modes, broadly used in the theory of multimode laser generation (12)- (16), in some cases allows assessing the generation dynamics qualitatively, but in the general case and for a

Cooperative Lamb shift for a cloud of two-level atoms located between two parallel-plate conductors

I give the closed-form analytic expression for the cooperative Lamb shift (CLS) in the scalar photon theory for an ensemble of two-level atoms in the shape of a slab located between two parallel-plate perfect conductors. I compute this quantity for the cases when the atomic system is initially prepared in a phased state and in the uniform state.

Thermalization of coupled atom-light states in the presence of optical collisions

The interaction of a two-level atomic ensemble with a quantized single mode electromagnetic field in the presence of optical collisions (OC) is investigated both theoretically and experimentally. The main accent is made on achieving thermal equilibrium for coupled atom-light states (in particular dressed states). We propose a model of atomic dressed state thermalization that accounts for the evolution of the pseudo-spin Bloch vector components and characterize the essential role of the spontaneous emission rate in the thermalization process. Our model shows that the time of thermalization of the coupled atom-light states strictly depends on the ratio of the detuning and the resonant Rabi frequency. The predicted time of thermalization is in the nanosecond domain and about ten times shorter than the natural lifetime at full optical power in our experiment. Experimentally we are investigating the interaction of the optical field with rubidium atoms in an ultra-high pressure buffer gas cell under the condition of large atom-field detuning comparable to the thermal energy in frequency units. In particular, an observed detuning dependence of the saturated lineshape is interpreted as evidence for thermal equilibrium of coupled atom-light states. A significant modification of sideband intensity weights is predicted and obtained in this case as well.

The metastable states in the cooperative emission from a system of two-level atoms in a sphere

The values of the radii of the sphere enclosing an ensemble of two-level atoms corresponding to metastable states in the cooperative emission are computed. The dynamics of these states and, in particular, the delay in the maximum of the emission intensity are given for the different orders of the critical radii. 1 The article is published in the original.

States of an Ensemble of Two-Level Atoms with Reduced Quantum Uncertainty

We generate entangled states of an ensemble of 5x10{4} 87Rb atoms by optical quantum nondemolition measurement. The resonator-enhanced measurement leaves the atomic ensemble, prepared in a superposition of hyperfine clock levels, in a squeezed spin state. By comparing the resulting reduction of quantum projection noise [up to 8.8(8) dB] with the concomitant reduction of coherence, we demonstrate a clock input state with spectroscopic sensitivity 3.0(8) dB beyond the standard quantum limit.

Quantum-information storage: A Schrödinger-picture approach

A theory is developed to obtain the state vector for an atom-field system in which a single-photon pulse propagates in an optically dense ensemble of two-level or three-level atoms. The manner in which the field and the atoms become entangled is described, as is the entanglement of the atoms produced by the radiation pulse. Two protocols for quantum-information storage are studied. In the first protocol, the single-photon pulse is totally absorbed in an ensemble of two-level atoms that are embedded in a dielectric host. To arrive at analytical expressions for the state vector, fluctuations of atomic position are neglected and it is assumed that the atoms' transition frequencies are inhomogeneously broadened with a width that is much larger than the bandwidth of the single-photon pulse. In the second protocol, a single-photon pulse is sent into a semi-infinite medium of three-level atoms under the conditions where electromagnetic-induced transparency can occur. It is shown that the usual results of pulse compression and reduced group velocity are recovered. Moreover, an explicit expression for the state vector of the atom-field system is obtained.

Enhanced Deflection of Light Ray by Atomic Ensemble on Coherent Population Oscillation

In recent experiments [e.g., Nature Physics 2 (2006) 332], the enhanced light deflection in an atomic ensemble due to inhomogeneous fields is demonstrated by the electromagnetically induced transparency (EIT) based mechanism. In this paper, we explore a different mechanism for the similar phenomenon of the enhanced light deflection. This mechanism is based on the coherent population oscillation, which leads to the hole burning in the absorption spectrum. The medium causing the deflection of probe light is an ensemble of two-level atoms manipulated by a strong controlled field on the two photon resonances. In the large detuning condition, the response of the medium to the pump field and signal field is obtained with steady state approximation. And it is found that after the probe field travels across the medium, the signal ray bends due to the spatial-dependent profile of the control beam.

Echo spectroscopy of atomic dynamics in a Gaussian trap via phase imprints

We report on the collapse and revival of Ramsey fringe visibility when a spatially dependent phase is imprinted in the coherences of a trapped ensemble of two-level atoms. The phase is imprinted via the light shift from a Gaussian laser beam which couples the dynamics of internal and external degrees of freedom for the atoms in an echo spectroscopy sequence. The observed revivals are directly linked to the oscillatory motion of atoms in the trap. An understanding of the effect is important for quantum state engineering of trapped atoms.

Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics

We develop practical schemes for the measurement of the covariance matrix for intrinsic angular-momentum variables in quantum optics. We particularize this approach to two-beam polarimetry and interferometry, as well as to ensembles of two-level atoms interacting with classical fields. We show the practical advantages of noisy simultaneous measurements.

Spontaneously induced atom–radiation entanglement in an ensemble of trapped two-level atoms

Analysis of the effects of the spontaneously induced correlation on atom–radiation entanglement in an ensemble of two-level atoms initially prepared in the upper energy level and then trapped in a cavity containing a source of a squeezed radiation employing the method of evaluating the coherent-state propagator is presented. It is found that the cavity radiation exhibits squeezing which is directly attributed to the squeezed radiation initially present in the cavity. The intensity of the cavity radiation increases with the squeeze parameter and interaction time. It is also shown that a substantial degree of entanglement between the atomic state and radiation mode exits at a particular time which depends on the coupling constant and squeeze parameter. It is understood that although the squeezed radiation is directly accountable for the cavity squeezing, it significantly destroys the atom–radiation entanglement induced by the correlation between spontaneously emitted radiation and the atoms.

Qutrits in multiparticle systems

The evolution of complex composite quantum systems which can be reduced to systems with a small dimensionality of the Hilbert space (of the qutrit, ququart type, etc.) is considered. In the case of the interaction of an ensemble of two-level atoms with light, the conditions are found under which a qutrit is produced from the light and atomic states. The properties and possible applications of a qutrit based of the Fock states of light in which two photons are distributed among three modes are discussed. It is shown that this state has the nonclassical photon statistics, is entangled and can be used as a quantum channel for the teleportation, dense coding, and key distribution.

Geometric manipulation of the population probability of two-level atoms and hybrid unitary operations of quantum states

The quantum states of cold ensemble of two-level atoms were rotated around axis 2 on the Bloch sphere geometrically using a laser-controlled resonant pulse sequence with pulse areas of $\ensuremath{\pi}∕2$, $\ensuremath{\pi}$, and $\ensuremath{\pi}∕2$, whose central pulse has a relative phase difference of $\ensuremath{\pi}+\ensuremath{\delta}∕2$. It was ascertained that the population probability of the excited state varies according to a sinusoidal function of $\ensuremath{\delta}$ within an uncertainty of 1%. Hybrid operations of two-level atoms were realized combining the geometrical operation with the Rabi excitation around axis 2 or the time evolution around axis 3.