Ensemble Of Two-level Atoms Research Articles

Optical properties of an atomic ensemble coupled to a band edge of a photonic crystal waveguide

We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole–dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the transmission spectrum contains multiple transmission dips, whose properties we characterize. Moreover, we show how the linear spectrum may be used to infer the number of atoms present in the system, constituting an important experimental tool in a regime where techniques for conventional ensembles break down. We also show that some of the transmission dips are associated with an effective ‘two-level’ resonance that forms due to the long-range interactions. In particular, under strong global driving and appropriate conditions, we find that the atomic ensemble is only capable of absorbing and emitting single collective excitations at a time. Our results are of direct relevance to atom-PCW experiments that should soon be realizable.

Superradiance enhancement by bad-cavity resonator

In this work we consider the dynamics of an ensemble of two-level atoms that interact with finite-width resonator mode. The superradiant burst occurs under a wide range of parameters in such a system. However, if the initial phase distribution of dipole moments of N two-level atoms is random, not all atoms take part in the superradiant process, but only the part of them that results in the intensity of supperradiance , where . In this paper we investigate the dependence of the parameter α on the resonator mode decay rate. It is shown that there is a critical value of resonator mode decay rate that divides two different regimes of superradiance. If the decay rate is lower than the critical rate, superradiance demonstrates a multi-peak character and the number of dipoles forming superradiant burst increases while α grows from 1 to 2. When the decay rate is larger than the critical value there is a single-peak superradiant regime. The delay time dependence on N changes from power to logarithmic law at the critical decay rate. The existence of the optimal value of resonator decay rate can be used for superradiance enhancement by a resonator with finite losses.

The X-like shaped spatiotemporal structure of the biphoton entangled state in a cold two-level atomic ensemble

We study the spatiotemporal structure of the biphoton entangled state generated by the four-wave mixing (FWM) process in a cold two-level atomic ensemble. We analyze, for the first time, the X-like shaped structure of the biphoton entangled state and the geometry of the biphoton correlation for different lengths and densities of the cold atomic ensemble. The propagation equations of the photon pairs generated from FWM process are derived in a spatiotemporal framework. By means of the input-output relations of the propagation equations, the biphoton amplitude function is obtained in a spatiotemporal domain. In the given frequency range, the biphoton amplitude displays an X-like shaped geometry, nonfactorizable in the space-time domain. Such an X-like shaped spatiotemporal structure is caused by the phase matching and the FWM gain. The former leads to the X-like shaped envelope of the biphoton correlation, while the latter gives rise to the oscillations around the X-like shaped envelope.

Dicke phase transition without total spin conservation

We develop a new fermionic path-integral formalism to analyze the phase diagram of open nonequilibrium systems. The formalism is applied to analyze an ensemble of two-level atoms interacting with a single-mode optical cavity, described by the Dicke model. While this model is often used as the paradigmatic example of a phase transition in driven-dissipative systems, earlier theoretical studies were limited to the special case when the total spin of the atomic ensemble is conserved. This assumption is not justified in most experimental realizations. Our new approach allows us to analyze the problem in a more general case, including the experimentally relevant case of dissipative processes that act on each atom individually and do not conserve the total spin. We obtain a general expression for the position of the transition, which contains as special cases the two previously known regimes: i) non-equilibrium systems with losses and conserved spin and ii) closed systems in thermal equilibrium and with the Gibbs ensemble averaging over the values of the total spin. We perform a detailed study of different types of baths and point out the possibility of a surprising non-monotonous dependence of the transition on the baths' parameters.

Cooperative effects and slow dynamics of fluorescence intensity from quantum emitters in a dielectric

We study theoretically the possibility of spontaneous switching between dim and bright fluorescence modes from a cooperative ensemble of two-level atoms driven by a cw-laser. A numerical analysis of transient regimes and transformations of the fluorescence spectrum are reported.

Noise squeezing of fields that bichromatically excite atoms in a cavity.

It is well known that bichromatic excitation on one common transition can tune the emission or absorption spectra of atoms due to the modulation frequency dependent non-linearities. However little attention has been focused on the quantum dynamics of fields under bichromatic excitation. Here we present dissipative effects on noise correlations of fields in bichromatic interactions with atoms in cavities. We first consider an ensemble of two-level atoms that interacts with the two cavity fields of different frequencies and considerable amplitudes. By transferring the atom-field nonlinearities to the dressed atoms we separate out the dissipative interactions of Bogoliubov modes with the dressed atoms. The Bogoliubov mode dissipation establishes stable two-photon processes of two involved fields and therefore leads to two-mode squeezing. As a generalization, we then consider an ensemble of three-level Λ atoms for cascade bichromatic interactions. We extract the Bogoliubov-like four-mode interactions, which establish a quadrilateral of the two-photon processes of four involved fields and thus result in four-mode squeezing.

Atom assisted cavity cooling of a micromechanical oscillator in the unresolved sideband regime

The ground state cooling of a mechanical oscillator in an optomechanical cavity containing an ensemble of identical two-level ground-state atoms is studied in the highly unresolved-sideband regime. The system exhibits electromagnetically-induced transparencylike quantum interference effect. The mutual interaction with the cavity optical field gives rise to an indirect coupling between the atomic and mechanical modes. In presence of this interaction, the noise spectrum gets modified and leads to asymmetric cooling and heating rates. Using the quantum master equation, time evolution of the average phonon number is studied and it is observed that the average phonon occupancy in the mechanical resonator exhibits ground-state cooling.

Towards strongly correlated photons in arrays of dissipative nonlinear cavities under a frequency-dependent incoherent pumping

We report a theoretical study of a quantum optical model consisting of an array of strongly nonlinear cavities incoherently pumped by an ensemble of population-inverted two-level atoms. Projective methods are used to eliminate the atomic dynamics and write a generalized master equation for the photonic degrees of freedom only, where the frequency-dependence of gain introduces non-Markovian features. In the simplest single cavity configuration, this pumping scheme gives novel optical bistability effects and allows for the selective generation of Fock states with a well-defined photon number. For many cavities in a weakly non-Markovian limit, the non-equilibrium steady state recovers a Grand-Canonical statistical ensemble at a temperature determined by the effective atomic linewidth. For a two-cavity system in the strongly nonlinear regime, signatures of a Mott state with one photon per cavity are found. Nous présentons l'étude d'un modèle d'optique quantique consistant en un réseau de cavités fortement non linéaires en présence de pompage incohérent induit par un ensemble d'atomes à deux niveaux, avec inversion de population. Nous appliquons une méthode projective afin d'éliminer les degrés de liberté atomiques, et dérivons une équation maîtresse généralisée contenant uniquement les degrés de liberté photoniques, dans laquelle le pompage dépendant de la fréquence induit des effets non markoviens. Dans le cas simple d'une cavité, cette méthode de pompage induit de nouveaux effets de bistabilité et permet la création d'états de Fock avec un nombre défini de photons. Dans le cas de plusieurs cavités dans un régime faiblement non markovien, l'état stationaire hors équilibre prend la forme d'un ensemble grand-canonique, dont la température effective est définie par la largeur du spectre d'émission des atomes. Dans une configuration à deux cavités, en régime fortement non linéaire, nous observons la signature d'un état de Mott avec un photon par site.

Simulating Dicke-like superradiance with classical light sources

In this paper we investigate the close relationship between Dicke superradiance, originally predicted for an ensemble of two-level atoms in entangled states, and the Hanbury Brown and Twiss effect, initially established in astronomy to determine the dimensions of classical light sources like stars. By studying the state evolution of the fields produced by classical sources -- defined by a positive Glauber-Sudarshan P function -- when recording intensity correlations of higher order in a generalized Hanbury Brown and Twiss setup we find that the angular distribution of the last detected photon, apart from an offset, is identical to the superradiant emission pattern generated by an ensemble of two-level atoms in entangled symmetric Dicke states. We show that the phenomenon derives from projective measurements induced by the measurement of photons in the far field of the sources and the permutative superposition of quantum paths identical to those leading to superradiance in the case of single photon emitters. We thus point out an important similarity between classical sources and quantum emitters upon detection of photons if the particular photon source remains unknown. We finally present a compact result for the characteristic functional which generates intensity correlations of arbitrary order for any kind of light sources.

High contrast all-optical diode based on direction-dependent optical bistability within asymmetric ring cavity**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274242, 11474221, and 11574229), the Joint Fund of the National Natural Science Foundation of China and the China Academy of Engineering Physics (Grant No. U1330203), and the National Key Basic Research Special Foundation of China (Grant

We propose a simple all-optical diode which is comprised of an asymmetric ring cavity containing a two-level atomic ensemble. Attributed to spatial symmetry breaking of the ring cavity, direction-dependent optical bistability is obtained in a classical bistable system. Therefore, a giant optical non-reciprocity is generated, which guarantees an all-optical diode with a high contrast up to 22 dB. Furthermore, its application as an all-optical logic AND gate is also discussed.

Controllable optical bistability in a hybrid optomechanical system

We investigate, theoretically, the effect of optical feedback from a cavity containing an ultracold two-level atomic ensemble, on the bistable behavior shown by a mean intracavity optical field in an optomechanical cavity resonator. It turns out that the optical bistability can be controlled by tuning the frequency and power of the driving laser and is largely affected by the presence of the atomic ensemble in the feedback cavity. In essence, our work emphasizes the possibility of realization of a controllable optical switch depending on the hybrid interaction, commanding lower threshold power than a single optomechanical cavity.

Thermalization and Bose–Einstein condensation of a photon gas in a multimode hybrid atom-membrane optomechanical microcavity

In this paper, we theoretically propose an optomechanical scheme to thermalize a two-dimensional photon gas in a hybrid optomechanical microcavity composed of a two-level atomic ensemble and a membrane oscillator enclosed in an optical cavity. The thermalization process is based on a phonon-induced asymmetry between the emission and the absorption rates of the atoms. We show that whenever this asymmetry obeys the detailed balance condition and if the photon lifetime is high enough, the steady-state photon number distribution matches the Bose–Einstein distribution. Furthermore, in order to study the effect of the optomechanical coupling on the Bose–Einstein condensation of photons, we calculate the critical photon number as a function of the temperature. We find that the optomechanically induced nonlinearity leads to the increase of the critical photon number, which can be controlled by tuning the optomechanical parameters.

Optical quantum memory for ultrafast photons using molecular alignment

The absorption of broadband photons in atomic ensembles requires either an effective broadening of the atomic transition linewidth, or an off-resonance Raman interaction. Here, we propose a scheme for a quantum memory capable of storing and retrieving ultrafast photons in an ensemble of two-level atoms using a propagation medium with a time–dependent refractive index generated from aligning an ensemble of gas-phase diatomic molecules. The refractive index dynamics generates an effective longitudinal inhomogeneous broadening of the two-level transition. We numerically demonstrate this scheme for storage and retrieval of a weak pulse as short as 50 fs, with a storage time of up to 20 ps. With additional optical control of the molecular alignment dynamics, the storage time can be extended about one nanosecond leading to time–bandwidth products of order 104. This scheme could in principle be achieved using either a hollow-core fibre or a high-pressure gas cell, in a gaseous host medium comprised of diatomic molecules and a two-level atomic vapour at room temperature.

Master equation for collective spontaneous emission with quantized atomic motion

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.

Single Photon Subradiance: Quantum Control of Spontaneous Emission and Ultrafast Readout.

Recent work has shown that collective single photon emission from an ensemble of resonate two-level atoms, i.e., single photon superradiance, is a rich field of study. The present Letter addresses the flip side of superradiance, i.e., subradiance. Single photon subradiant states are potentially stable against collective spontaneous emission and can have ultrafast readout. In particular it is shown how many atom collective effects provide a new way to control spontaneous emission by preparing and switching between subradiant and superradiant states.

Superbunching and Nonclassicality as new Hallmarks of Superradiance.

Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.

Ground-state cooling of an optomechanical resonator assisted by an atomic ensemble

We investigate a ground-state cooling scheme for a mechanical resonator assisted by one two-level atomic ensemble. The atomic ensemble is confined in the optomechanical cavity and strongly couples to the cavity mode. Our scheme works in a strong excitation of the system. Thus, there are enough photons in the cavity to produce coupling between the mechanical and optical degrees of freedom. It is shown that our scheme can work well in the unresolved sideband regime and can accelerate the cooling process.

Vacuum induced transparency and slow light phenomena in a two-level atomic ensemble controlled by a cavity**Project supported by the National Natural Science Foundation of China (Grant No. 11304010).

We study the optical properties of a two-level atomic ensemble controlled by a high-finesse cavity. Even though the cavity is initially in the vacuum state in the absence of external driving, the probe response of the atomic ensemble can be dramatically modified. When the collectively enhanced atom–cavity coupling is strong enough and the cavity decay rate is much smaller than the atomic damping rate, an electromagnetically induced transparency-like coherent phenomenon emerges with a dip absorption for the response of the two-level atoms in the cavity without driving, and thus is called vacuum induced transparency. We also show the slow light with very low group velocity in such an atomic ensemble.

Conditional ramsey spectroscopy with synchronized atoms.

We investigate Ramsey spectroscopy performed on a synchronized ensemble of two-level atoms. The synchronization is induced by the collective coupling of the atoms to a heavily damped mode of an optical cavity. We show that, in principle, with this synchronized system it is possible to observe Ramsey fringes indefinitely, even in the presence of spontaneous emission and other sources of individual-atom dephasing. This could have important consequences for atomic clocks and a wide range of precision metrology applications.

Directional superradiant emission from statistically independent incoherent nonclassical and classical sources.

Superradiance has been an outstanding problem in quantum optics since Dicke introduced the concept of enhanced directional spontaneous emission by an ensemble of identical two-level atoms. The effect is based on the correlated collective Dicke states which turn out to be highly entangled. Here we show that enhanced directional emission of spontaneous radiation can be produced also with statistically independent incoherent sources, via the measurement of higher-order correlation functions of the emitted radiation. Our analysis is applicable to a wide variety of quantum emitters, like trapped atoms, ions, quantum dots, or nitrogen-vacancy centers, and is also valid for incoherent classical emitters. This is experimentally confirmed with up to eight statistically independent thermal light sources. The arrangement to measure the higher-order correlation functions corresponds to a generalized Hanbury Brown-Twiss setup, demonstrating that the two phenomena, superradiance and the Hanbury Brown-Twiss effect, stem from the same interference phenomenon.