We experimentally demonstrate optical dipole trapping of a cloud of cold atoms by means of a dynamically coupled mode of a high-finesse cavity. We show that the trap requires a collective action of the atoms, i.e. a single atom would not be trapped under the same laser drive conditions. The atoms pull the frequency of the mode closer to resonance, thereby allowing the necessary light intensity for trapping into the cavity. The back-action of the atoms on the trapping light mode is also manifested by the non-exponential collapse of the trap.
By integrating the techniques of laser cooling and trapping with those of cavity quantum electrodynamics (QED), single Cesium atoms have been trapped within the mode of a small, high finesse optical cavity in a regime of strong coupling. The observed lifetime for individual atoms trapped within the cavity mode is $τ\approx 28$ms, and is limited by fluctuations of light forces arising from the far-detuned intracavity field. This initial realization of trapped atoms in cavity QED should enable diverse protocols in quantum information science.
The aim of this work is to find ways to trap an atom in a cavity. In contrast to other approaches we propose a method where the cavity is basically in the vacuum state and the atom in the ground state. The idea is to induce a spatial dependent AC Stark shift by irradiating the atom with a weak laser field, so that the atom experiences a trapping force. The main feature of our setup is that dissipation can be strongly suppressed. We estimate the lifetime of the atom as well as the trapping potential parameters and compare our estimations with numerical simulations.
In population trapping the occupation of a decaying quantum level keeps a constant non-zero value. We show that an atom-cavity system interacting with an environment characterized by a non-flat spectrum, in the non-Markovian limit, exhibits such a behavior, effectively realizing the preservation of nonclassical states against dissipation. Our results allow to understand the role of cavity losses in hybrid solid state systems and pave the way to the proper description of leakage in the recently developed cavity quantum electrodynamic systems.
We investigate signals of trapping states in the micromaser system in terms of the average number of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for even for a mean number of atoms inside the cavity close to one. We, however,…
We study analytically the dynamics of cavity QED nodes in a practical quantum network. Given a single 3-level $Λ$-type atom or quantum dot coupled to a micro-cavity, we derive several necessary and sufficient criteria for the coherent trapping and generation of a single photon pulse with a given waveform to be realizable. We prove that these processes can be performed with practical hardware -- such as cavity QED systems which are operating deep in the weak coupling regime -- given a set of restrictions on the single-photon pulse envelope. We systematically study the effects of spontaneous emi…
We consider a coupled-cavity array (CCA), where one cavity interacts with a two-level atom under the rotating-wave approximation. We investigate the excitation transport dynamics across the array, which arises in the atom's emission process into the CCA vacuum. Due to the known formation of atom-photon bound states, partial field localization and atomic population trapping in general take place. We study the functional dependance on the coupling strength of these two phenomena and show that the threshold values beyond which they become significant are different. As the coupling strength grows …
Single Cesium atoms are cooled and trapped inside a small optical cavity by way of a novel far-off-resonance dipole-force trap (FORT), with observed lifetimes of 2 to 3 seconds. Trapped atoms are observed continuously via transmission of a strongly coupled probe beam, with individual events lasting ~ 1 s. The loss of successive atoms from the trap N = 3 -> 2 -> 1 -> 0 is thereby monitored in real time. Trapping, cooling, and interactions with strong coupling are enabled by the FORT potential, for which the center-of-mass motion is only weakly dependent on the atom's internal state.
We show that high squeezing and entanglement can be generated at the output of a cavity containing atoms interacting with two fields in a Coherent Population Trapping situation, on account of a non-linear Faraday effect experienced by the fields close to a dark-state resonance in a cavity. Moreover, the cavity provides a feedback mechanism allowing to reduce the quantum fluctuations of the ground state spin, resulting in strong steady state spin-squeezing.
Optomechanical systems have been attracting intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it, and impos…
We describe how quantum dot semiconductor cavity systems can be engineered to realize anisotropy-induced dipole-dipole coupling between orthogonal dipole states in a single quantum dot. Quantum dots in single-mode cavity structures as well as photonic crystal waveguides coupled to spin states or linearly polarized excitons are considered. We demonstrate pronounced dipole-dipole coupling to control the radiative decay rate of excitons and form pure entangled states in the long time limit. We investigate both field-free entanglement evolution and coherently pumped exciton regimes, and show how a…
A cold atomic gas with an inverted population on a transition coupled to a field mode of an optical resonator constitutes a generic model of a laser. For quasi-continuous operation, external pumping, trapping and cooling of the atoms is required to confine them in order to achieve enough gain inside the resonator. As inverted atoms are high-field seekers in blue detuned light fields, tuning the cavity mode to the blue side of the atomic gain transition allows for combining lasing with stimulated cavity cooling and dipole trapping of the atoms at the antinodes of the laser field. We study such …
A single atom strongly coupled to a cavity mode is stored by three-dimensional confinement in blue-detuned cavity modes of different longitudinal and transverse order. The vanishing light intensity at the trap center reduces the light shift of all atomic energy levels. This is exploited to detect a single atom by means of a dispersive measurement with 95% confidence in 0.010 ms, limited by the photon-detection efficiency. As the atom switches resonant cavity transmission into cavity reflection, the atom can be detected while scattering about one photon.
In a hybrid micromaser system consisting of an optical cavity with a moving mirror connected to a low temperature thermal bath, we demonstrate, both analytically and numerically, that for certain interaction times between a random atomic flux and the optomechanical cavity, vacuum phonon trapping states are generated. Furthermore, under the approach of the master equation with independent phonon and photon thermal baths, we show that the trapping of the phonons and photons is achieved for the same interaction times. The results also indicate that by increasing the cavity-oscillator coupling one…
We analyzed the efficiency of coherent population trapping (CPT) in a superposition of the ground states of three-level atoms under the influence of the decoherence process induced by a broadband thermal field. We showed that in a single atom there is no perfect CPT when the atomic transitions are affected by the thermal field. The perfect CPT may occur when only one of the two atomic transitions is affected by the thermal field. In the case when both atomic transitions are affected by the thermal field, we demonstrated that regardless of the intensity of the thermal field the destructive effe…
We investigate cooling and trapping of single atoms inside an optical cavity using a quasi-resonant field and a far-off resonant mode of the Laguerre-Gauss type. The far-off resonant doughnut mode provides an efficient trapping in the case when it shifts the atomic internal ground and excited state in the same way, which is particularly useful for quantum information applications of cavity quantum electrodynamics (QED) systems. Long trapping times can be achieved, as shown by full 3-D simulations of the quasi-classical motion inside the resonator.
We consider the situation where a two-level atom is placed in the vicinity of the center of a spherical cavity with a large numerical aperture. The vacuum field at the center of the cavity is actually equivalent to the one obtained in a microcavity, and both the dissipative and the reactive parts of the atom's spontaneous emission are significantly modified. Using an explicit calculation of the spatial dependence of the radiative relaxation rate and of the associated level shift, we show that for a weakly excitating light field, the atom can be attracted to the center of the cavity by vacuum-i…
Taming quantum dynamical processes is the key to novel applications of quantum physics, e.g. in quantum information science. The control of light-matter interactions at the single-atom and single-photon level can be achieved in cavity quantum electrodynamics, in particular in the regime of strong coupling where atom and cavity form a single entity. In the optical domain, this requires permanent trapping and cooling of an atom in a micro-cavity. We have now realized three-dimensional cavity cooling and trapping for an orthogonal arrangement of cooling laser, trap laser and cavity vacuum. This l…
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000) and Pinkse et al., Nature 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. Firstly, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts. Secondly, we explore the quantitative features of the resulting atomic motion and how these dynamics are mapped onto variations of the in…
Cavity cooling of an atom works best on a cyclic optical transition in the strong coupling regime near resonance, where small cavity photon numbers suffice for trapping and cooling. Due to the absence of closed transitions a straightforward application to molecules fails: optical pumping can lead the particle into uncoupled states. An alternative operation in the far off-resonant regime generates only very slow cooling due to the reduced field-molecule coupling. We predict to overcome this by using a strongly driven ring-cavity operated in the sideband cooling regime. As in the optomechanical …
We investigate the transmission spectrum of an optical cavity coupled with four-level atoms. Multiple normal-mode splitting peaks of the strongly coupled atom-cavity system are obtained as single cavity mode couples three separated atomic transitions simultaneously. We employ a confocal optical cavity and an ensemble of cold Rb-85 atoms for cavity quantum electrodynamics. We observe four normal-mode splitting peaks of the cavity transmission in the strong coupling regime due to collective enhancement of the atom-cavity coupling strength by ensemble of cold atoms. The experimental observations …
We analyze a possibility to trap, control and load a single atom inside a nanosize cavity formed in a photonic crystal. We consider a 1D nanobeam crystal having two nearly degenerate localized modes with mode maxima at the central air gap, forming a cavity with a mode volume <λ^{3}. For this system we found that an atom can be trapped by a mode detuned from an atomic transition and controled by the second resonant mode. We show that atomic motion can be cooled using cavity-enhanced rf Sisyphus cooling. We also discuss how an atom can be loaded inside the nanosize crystal air gap from short-wav…
We study collective effects in an inhomogeneously broadened ensemble of two-level emitters coupled to an optical cavity with narrow linewidth. Using second order mean field theory we find that the emitters within a few times the cavity linewidth exhibit synchronous behaviour and undergo collective Rabi oscillations. Under proper conditions, the synchronized oscillations give rise to a modulated intracavity field which can excite emitters detuned by many linewidths from the cavity resonance. To study the synchronization in further detail, we simplify the model and consider two ensembles and stu…
We study the transmission spectra of ultracold rubidium atoms coupled to a high-finesse optical cavity. Under weak probing with pi-polarized light, the linear response of the system is that of a collective spin with multiple levels coupled to a single mode of the cavity. By varying the atom number, we change the collective coupling of the system. We observe the change in transmission spectra when going from a regime where the collective coupling is much smaller than the separation of the atomic levels to a regime where both are of comparable size. The observations are in good agreement with a …
This paper discusses a collective quantum effect which might play an important role in sonoluminescence experiments. We suggest that it occurs during the final stages of the collapse phase and enhances the heating of the particles inside the bubble.
A collective system of atoms in a high quality cavity can be described by a nonlinear interaction which arises due to the Lamb shift of the energy levels due to the cavity vacuum [Agarwal et al., Phys. Rev. A 56, 2249 (1997)]. We show how this collective interaction can be used to perform quantum logic. In particular we produce schemes to realize CNOT gates not only for two-qubit but also for three-qubit systems. We also discuss realizations of Toffoli gates. Our effective Hamiltonian is also realized in other systems such as trapped ions or magnetic molecules.
We report the development of quantum microscopic theory of quasi-resonant dipole-dipole interaction in the ensembles of impurity atoms imbedded into transparent dielectric and located into Fabry-Perot cavity. On the basis of the general approach we study the simultaneous influence of the cavity and resonant dipole-dipole interaction on the shape of the line of atomic transition as well as on light trapping in dense impurity ensembles. We analyze this influence depending on the size of the ensemble, its density, as well as on r.m.s. deviation of the transition frequency shifts caused by the sym…
When N driven atoms emit in phase into a high-Q cavity mode, the intracavity field generated by collective scattering interferes destructively with the pump driving the atoms. Hence atomic fluorescence is suppressed and cavity loss becomes the dominant decay channel for the whole ensemble. Microscopically 3D light-intensity minima are formed in the vicinity of the atoms that prevent atomic excitation and form a regular lattice. The effect gets more pronounced for large atom numbers, when the sum of the atomic decay rates exceeds the rate of cavity losses and one would expect the opposite behav…
We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full 3-D simulations of the quasiclassical motion of a Cs atom are performed.
We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number…
We report on collective non-linear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retro-action of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Non-adiabatic aspects of the atomic motion are reproduced by solving the complete system of cou…
Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity $C$, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, $C$ is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)] we have shown that collective excitations in ensembles of dipole-dipole coupled qu…
We present a study of collapse-revival patterns that appear in the changes of atomic populations induced by the interaction of ultracold two-level atoms with electromagnetic cavities in resonance with an $m$-photon transition of the atoms ($m$-photon mazer). In particular, sech$^2$ and gaussian cavity mode profiles are considered and differences in the collapse-revival patterns are reported. The quantum theory of the $m$-photon mazer is written in the framework of the dressed-state coordinate formalism. Simple expressions for the atomic populations, the cavity photon statistics, and the reflec…
We analyze the magnetic dipole coupling of an ensemble of spins to a superconducting microwave stripline structure, incorporating a Josephson junction based transmon qubit. We show that this system is described by an embedded Jaynes-Cummings model: in the strong coupling regime, collective spin-wave excitations of the ensemble of electrons pick up the nonlinearity of the cavity mode, such that the two lowest eigenstates of the coupled spin-wave + microwave-cavity + Josephson-junction system define a hybrid two-level system. The proposal described here enables the use of spin ensembles as qubit…
We report on Kerr nonlinearity and dispersive optical bistability of a Fabry-Perot optical resonator due to the displacement of ultracold atoms trapped within. In the driven resonator, such collective motion is induced by optical forces acting upon up to $10^5$ $^{87}$Rb atoms prepared in the lowest band of a one-dimensional intracavity optical lattice. The longevity of atomic motional coherence allows for strongly nonlinear optics at extremely low cavity photon numbers, as demonstrated by the observation of both branches of optical bistability at photon numbers below unity.
We theoretically investigate an ensemble of three-level room-temperature atoms in a two-mode optical cavity, focusing on the case of counterpropagating light fields. We find that in the limit of large detunings the problem admits relatively simple and intuitive solutions. When a classical field drives one of the transitions, the system becomes equivalent to an ensemble of two-level atoms with suppressed Doppler broadening. In contrast, when the same transition is driven with a single photon, the system collectively behaves like a single two-level atom. This latter result is particularly releva…
We report the observation of collective-emission-induced, velocity-dependent light forces. One third of a falling sample containing 3 x 10^6 cesium atoms illuminated by a horizontal standing wave is stopped by cooperatively emitting light into a vertically oriented confocal resonator. We observe decelerations up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the free space Doppler limit. The measured forces substantially exceed those predicted for a single two-level atom.
A scheme for engineering quantum interference in a $Λ$-type atom coupled to a frequency-tunable, single-mode cavity field with a pre-selected polarization at finite temperature is proposed. Interference-assisted population trapping, population inversions and probe gain at one sideband of the Autler-Townes spectrum are predicted for certain cavity resonant frequencies.
We investigate the coherent manipulation of interacting Rydberg atoms placed inside a high-finesse optical cavity for the deterministic preparation of strongly coupled light-matter systems. We consider a four-level diamond scheme with one common Rydberg level for N interacting atoms. One side of the diamond is used to excite the atoms into a collective `superatom' Rydberg state using either π-pulses or stimulated Raman adiabatic passage (STIRAP) pulses. The upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an op…
We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. \textbf{99}, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson \textit{et al.}, arXiv:0707.1724v2, 2007]. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effe…
In the absence of time-reversal symmetry, the asymmetric parameter q of the Fano resonance is extended into the complex space, where its trajectory can be utilized to investigate the decoherence process. By embedding the ensemble of M$\ddot{\rm{o}}$ssbauer nuclei in the thin-film planar cavity in this work, the trajectories of asymmetric parameter q are studied via the collective effect of the nuclear ensemble, which is regulated by the nuclear abundance and angle offset. Due to the diverse controllable methods of the collective resonant strength, there are different straight lines and arc-sha…
Electromagnetically induced transparency (EIT) is an optical phenomenon which allows a drastic modification of the optical properties of an atomic system by applying a control field. It has been largely studied in the last decades and nowadays we can find a huge number of experimental and theoretical related studies. Recently a similar phenomenon was also shown in quantum dot molecules (QDM) , where the control field is replaced by the tunneling rate between quantum dots. Our results show that in the EIT regime, the optical properties of QDM and the atomic system are identical. However, here w…
We propose a cavity based laser cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave which acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate travelling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high frequency component, that is tuned to the anti-Stokes Raman sideband of the particl…
We investigate the suppression of spontaneous emission from a driven three-level system embedded in an optical cavity via a manifestation of the quantum Zeno effect. Strong resonant coupling of the lower two levels to an external optical field results in a decrease of the exponential decay rate of the third upper level. We show that this effect has observable consequences in the form of emission spectra with subnatural linewidths, which should be measurable using, for example, quantum dot--cavity systems in currently obtainable parameter regimes. These results constitute a novel method to cont…
We propose and analyze a simple method to squeeze dynamically and unconditionally the collective spin of a dilute atomic ensemble by interaction with a driven mode of an optical resonator, as recently demonstrated [I. D. L., M. H. S., and V. V., Phys. Rev. Lett. 104, 073602 (2010)]. We show that substantial squeezing can be achieved in the regime of strong collective ensemble-resonator coupling. The squeezing is ultimately limited either by photon emission into free space or by the curvature of the Bloch sphere. We derive both limits and show where each prevails.
We report on the observation of cooperative radiation of exactly two neutral atoms strongly coupled to the single mode field of an optical cavity, which is close to the lossless-cavity limit. Monitoring the cavity output power, we observe constructive and destructive interference of collective Rayleigh scattering for certain relative distances between the two atoms. Because of cavity backaction onto the atoms, the cavity output power for the constructive two-atom case ($N=2$) is almost equal to the single-emitter case ($N=1$), which is in contrast to free-space where one would expect an $N^2$ …
A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of [P. F. Herskind et al., Nature Phys. 5, 494 (2009)] and of complementary new measurements. Gene…
We study the collective motion of atoms confined in an optical lattice operating inside a high finesse ring cavity. A simplified theoretical model for the dynamics of the system is developed upon the assumption of adiabaticity of the atomic motion. We show that in a regime where the light shift per photon times the number of atoms exceeds the line width of the cavity resonance, the otherwise tiny retro-action of the atoms upon the light field becomes a significant feature of the system, giving rise to dispersive optical bistability of the intra-cavity field. A solution of the complete set of c…
In this paper, we investigate theoretically the back-action evading measurement of the collective mode of an interacting atomic Bose-Einstein condensate (BEC) trapped in an optical cavity which is driven coherently by a pump laser with a modulated amplitude. It is shown that for a specified kind of amplitude modulation of the driving laser, one can measure a generalized quadrature of the collective mode of the BEC indirectly through the output cavity field with a negligible backaction noise in the good-cavity limit. Nevertheless, the on-resonance added noise of measurement is suppressed below …
We study the quantum statistical properties of the collective excitations of an atomic ensemble inside a high-finesse cavity. In the large-detuning regime, it is found that the virtual photon exchange can induce a long-range interaction between atoms, which results in correlated excitations. In particular, the atomic blockade phenomenon occurs when the induced long-range interaction effectively suppresses the double atomic excitation, when the average photon number takes certain values, which makes the two nearest energy levels degenerate. We also show that quantum phase transitions occur in t…
In this paper, we identify a many-particle phonon expectation value $ζ$ with the ability to induce collective dynamics in a non-interacting atomic gas inside an optical cavity. We then propose to utilise this expectation value to enhance the laser cooling of many atoms through a cyclic two-stage process which consists of cooling and displacement stages. During cooling stages, short laser pulses are applied. These use $ζ$ as a resource and decrease the vibrational energy of the atomic gas by a fixed amount. Subsequent displacement stages use the asymmetry of the trapping potential to replenish …
