We consider the effects of the trap environment on the atomic and optical quantum statistical properties and on the atom-photon correlations in the Collective Atomic-Recoil Laser. Atomic and optical statistical properties, as well as the atom-photon correlations are dependent on the optical field intensity and phase. In particular, depending on the values of the optical field intensity and phase, the fields statistics varies from coherent to superchaotic.
The recoil of atoms in arrays due to the emission or absorption of photons is studied for sub-wavelength interatomic spacing. The atoms in the array interact with each other through collective dipole-dipole interactions and with the incident laser field in the low intensity limit. Shining uniform light on the array gives rise to patterns of excitation and recoil in the array. These arise due to the interference of different eigenmodes of excitation. The relation between the recoil and the decay dynamics is studied when the array is in its excitation eigenstates. The recoil experienced by a sub…
Self-organization effects related to light amplification in the collective atomic recoil laser system with the driven atoms confined in a harmonic trap are investigated further. In the dispersive parametric region, our study reveals that the spontaneously formed structures in the phase space contributes an important role to the light amplification of the probe field under the atomic motion being modified by the trap.
We observe the buildup of a frequency-shifted reverse light field in a unidirectionally pumped high-$Q$ optical ring cavity serving as a dipole trap for cold atoms. This effect is enhanced and a steady state is reached, if via an optical molasses an additional friction force is applied to the atoms. We observe the displacement of the atoms accelerated by momentum transfer in the backscattering process and interpret our observations in terms of the collective atomic recoil laser. Numerical simulations are in good agreement with the experimental results.
We formulate a wave atom optics theory of the Collective Atomic Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. By comparing the predictions of this theory with those of the ray atom optics theory, which treats the center-of-mass motion classically, we show that for the case of a far off-resonant pump laser the ray optics model fails to predict the linear response of the CARL when the temperature is of the order of the recoil temperature or less. This is due to the fact that in theis temperature regime one can no longer ignore the effects of matter-wave di…
We demonstrate optical nonlinearities due to the interaction of weak optical fields with the collective motion of a strongly dispersive ultracold gas. The combination of a recoil-induced resonance (RIR) in the high gain regime and optical waveguiding within the dispersive medium enables us to achieve a collective atomic cooperativity of $275 \pm 50$ even in the absence of a cavity. As a result, we observe optical bistability at input powers as low as 20 pW. The present scheme allows for dynamic optical control of the dispersive properties of the ultracold gas using very weak pulses of light. T…
We demonstrate clear collective atomic recoil motion in a dilute, momentum-squeezed, ultra-cold degenerate fermion gas by circumventing the effects of Pauli blocking. Although gain from bosonic stimulation is necessarily absent because the quantum gas obeys Fermi-Dirac statistics, collective atomic recoil motion from the underlying wave-mixing process is clearly visible. With a single pump pulse of the proper polarization, we observe two mutually-perpendicular wave-mixing processes occurring simultaneously. Our experiments also indicate that the red-blue pump detuning asymmetry observed with B…
We extend the Collective Atomic Recoil Lasing (CARL) model including the effects of friction and diffusion forces acting on the atoms due to the presence of optical molasses fields. The results from this model are consistent with those from a recent experiment by Kruse et al. [Phys. Rev. Lett. 91, 183601 (2003)]. In particular, we obtain a threshold condition above which collective backscattering occurs. Using a nonlinear analysis we show that the backscattered field and the bunching evolve to a steady-state, in contrast to the non-stationary behaviour of the standard CARL model. For a proper …
Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are described by the same model of classical equations for properly defined scaled variables. These equations are extended to the quantum domain describing the particle's motion by a Schrödinger equation coupled to a self-consistent radiation field. The model depends on a single collective parameter $\bar ρ$ which represents the maximum number of photons emitted per particle. We demonstrate that the classical model is recovered in the limit $\bar ρ\gg 1$, in which the Wigner function associated to the Schrödinger equation obey…
Networks of globally coupled oscillators exhibit phase transitions from incoherent to coherent states. Atoms interacting with the counterpropagating modes of a unidirectionally pumped high-finesse ring cavity form such a globally coupled network. The coupling mechanism is provided by collective atomic recoil lasing (CARL), i.e. cooperative Bragg scattering of laser light at an atomic density grating, which is self-induced by the laser light. Under the rule of an additional friction force, the atomic ensemble is expected to undergo a phase transition to a state of synchronized atomic motion. We…
The recoil effects of spontaneous photon emissions during optical pumping of a trapped three-level atom are exactly calculated. Without resort to the Lamb-Dicke approximation, and considering arbitrary detuning and saturation of the pump laser, the density of recoil shifts in phase space is derived. It is shown that this density is not of Gaussian shape, and that it becomes isotropic in phase space only for a branching ratio corresponding to fluorescence scattering but unfavorable for optical pumping. The dependence of its anisotropy on the laser saturation is discussed in the resonant case, a…
We propose an experiment to realize radiation to atom continuous variable quantum mapping, i.e. to teleport the quantum state of a single mode radiation field onto the collective state of atoms with a given momentum out of a Bose-Einstein condensate. The atoms-radiation entanglement needed for the teleportation protocol is established through the interaction of a single mode with the condensate in presence of a strong far off-resonant pump laser, whereas the coherent atomic displacement is obtained by the same interaction with the radiation in a classical coherent field. In principle, verifica…
We present a wave atom optics theory of the Collective Atomic-Recoil Laser, where the atomic center-of-mass motion is treated quantum mechanically. It extends the previous ray atom optics theory, which treated the center-of-mass atomic motion classically, to the realm of ultracold atoms. For the case of a far off resonant pump laser we derive an analytical solution which gives the linear response of the CARL system for both the quantum and classical regimes. A linear stability analysis reveals significant qualitative differences between these two regimes, which arise from the effects of diffra…
We describe a method for non-degenerate four-wave mixing in a cold sample of 4-level atoms. An integral part of the four-wave mixing process is a collective instability which spontaneously generates a periodic density modulation in the cold atomic sample with a period equal to half of the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase-matching between the pump and scattered fields is not a necessary initial condition for this wave-mixing process to occur, rather the density modulation acts to "self phase-match" the fields durin…
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits …
We study a system represented by a Bose-Einstein condensate interacting with a cavity field in presence of a strong off-resonant pumping laser. This system can be described by a three-mode Gaussian state, where two are the atomic modes corresponding to atoms populating upper and lower momentum sidebands and the third mode describes the scattered cavity field light. We show that, as a consequence of the collective atomic recoil instability, these modes possess a genuine tripartite entanglement that increases unboundedly with the evolution time and is larger than the bipartite entanglement in an…
The scattering of a single photon with sufficiently high energy can cause a recoil of a motional scatterer. We study its backaction on the photon's coherent transport in one dimension by modeling the motional scatterer as a two-level system, which is trapped in a harmonic potential. While the reflection spectrum is of a single peak in the Lamb-Dicke limit, multi-peaks due to phonon excitations can be observed in the reflection spectrum as the trap becomes looser or the mass of the two-level system becomes smaller.
An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in signific…
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.
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,…
Spatial correlation functions provide a glimpse into the quantum correlations within a quantum system. Ions in a linear trap collectively form a nonuniform, discretized background on which a scalar field of phonons propagates. Trapped ions have the experimental advantage of each having their own "built-in" motional detector: electronic states that can be coupled, via an external laser, to the ion's vibrational motion. The post-interaction electronic state can be read out with high efficiency, giving a stochastic measurement record whose classical correlations reflect the quantum correlations o…
The angle and temperature dependence of the photon scattering rate for Bose-stimulated atom recoil transitions between occupied states is compared to diffraction and incoherent Rayleigh scattering near the Bose-Einstein transition for an optically thin trap in the limit of large particle number, N. Each of these processes has a range of angles and temperatures for which it dominates over the others by a divergent factor as N->oo.
We analyse the effects of atom-atom collisions on collective laser cooling scheme. We derive a quantum Master equation which describes the laser cooling in presence of atom-atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose-Einstein distribution describing collisionally induced equilibrium,to a distribution with an effective zero tempera…
We show that the slow driving of a focused laser beam through the cloud of trapped cold fermions allows for a creation of the collective excitation in the system. The method, proposed originally by us for bosons, seems to be quite feasible experimentally -- it requires only an appropriate change in time of the potential in atomic traps, as realized in laboratories already.
A mean field theory for Raman superradiance (SR) with recoil is presented, where the typical SR signatures are recovered, such as quadratic dependence of the intensity on the number of atoms and inverse proportionality of the time scale to the number of atoms. A comparison with recent experiments and theories on Rayleigh SR and collective atomic recoil lasing (CARL) are included. The role of recoil is shown to be in the decay of atomic coherence and breaking of the symmetry of the SR end-fire modes.
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 report preparation in the ground state of collective modes of motion of two trapped 9Be+ ions. This is a crucial step towards realizing quantum logic gates which can entangle the ions' internal electronic states. We find that heating of the modes of relative ion motion is substantially suppressed relative to that of the center-of-mass modes, suggesting the importance of these modes in future experiments.
A simple technique for robust generation of vibrational Fock states in a chain of trapped ions is proposed. The method is fast and easy to implement, since only a single chirped laser pulse, simultaneously addressing all of the ions, is required. Furthermore, because the approach uses collective adiabatic passage, significant fluctuations in the intensity or frequency of the laser pulse can be tolerated, and the technique performs well even on the border of the Lamb-Dicke regime. We also demonstrate how this technique may be extended in order to create non-classical superposition states of the…
We study the richer structures of quasi-one-dimensional Bogoliubov-de Genes collective excitations of F = 1 spinor Bose-Einstein condensate in a harmonic trap potential loaded in an optical lattice. Employing a perturbative method we report general analytical expressions for the confined collective polar and ferromagnetic Goldstone modes. In both cases the excited eigenfrequencies are given as function of the 1D effective coupling constants, trap frequency and optical lattice parameters. It is shown that the main contribution of the optical lattice laser intensity is to shift the confined phon…
We show that it is possible to ``store'' quantum states of single-photon fields by mapping them onto {\it collective} meta-stable states of an optically dense, coherently driven medium inside an optical resonator. An adiabatic technique is suggested which allows to transfer non-classical correlations from traveling-wave single-photon wave-packets into atomic states and vise versa with nearly 100% efficiency. In contrast to previous approaches involving single atoms, the present technique does not require the strong coupling regime corresponding to high-Q micro-cavities. Instead, intracavity El…
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 …
In photon recoil spectroscopy, signals are extracted from recoils imparted by the spectroscopy light on the motion of trapped ions as demonstrated by C. Hempel et al., Nature Photonics 7, 630 (2013) and Y. Wan et al., Nature Communications 5, 3096 (2014). The method exploits the exquisite efficiency in the detection of phonons achievable in ion crystals, and is thus particularly suitable for species with broad non-cycling transitions where detection of fluorescence photons is impractical. Here, we develop a theoretical model for the description of photon recoil spectroscopy based on a Fokker-P…
Collective coherent scattering of laser light induces strong light forces between polarizable point particles. These dipole forces are strongly enhanced in magnitude and distance within the field of an optical waveguide so that at low temperature the particles self-order in strongly bound regular patterns. The stationary configurations typically exhibit super-radiant scattering with strong particle and light confinement. Here we study collective excitations of such self-consistent crystalline particle-light structures as function of particle number and pump strength. Multiple scattering and ab…
Collective Dissipation and Parameter Sensitivity in Trapped Ions Coupled to a Common Thermal Reservoir
Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas（坎皮纳斯州立大学格莱布·瓦塔金物理研究所）；Departamento de Administração, FEA-RP, Universidade de São Paulo（圣保罗大学雷班普雷图经济与管理学院行政管理系）
Resonant dipole-dipole interaction modifies the energy and decay rate of electronic excitations for finite one dimensional chains of ultracold atoms in an optical lattice. We show that collective excited states of the atomic chain can be divided into dark and bright modes, where a superradiant mode with an enhanced collective effective dipole dominates the optical scattering. Studying the generic case of two chain segments of different length and position exhibits an interaction blockade and spatially structured light emission. Ultimately, an extended system of several interfering segments mod…
We consider physical processes caused by the twisted photons for a wide range of energy scales, from optical (eV) to nuclear (MeV) to high-energy gamma-rays (TeV). We demonstrate that in order to satisfy angular momentum conservation, absorption of a twisted photon leads to a transverse recoil of the final particle or a system of particles leading to increased threshold energy required for the reaction to proceed. Modification of the threshold energy is predicted for (a) Photo-absorption on colds trapped ions of $^{40}$Ca, along with emerging new transverse-motion sidebands, (b) photo-disinteg…
We study point-like polarizable particles confined in a 1D very elongated trap within the evanescent field of an optical nano-fiber or nano-structure. When illuminated transversely by coherent light, collective light scattering into propagating fiber modes induces long range interactions and eventually crystallisation of the particles into regular order. We develop a simple and intuitive scattering-matrix based approach to study these long-range interactions by collective scattering and the resulting light-induced self-ordering. For few particles we derive explicit conditions for self-consiste…
Ordered atomic arrays trapped in the vicinity of nanoscale waveguides offer original light-matter interfaces, with applications to quantum information and quantum non-linear optics. Here, we study the decay dynamics of a single collective atomic excitation coupled to a waveguide in different configurations. The atoms are arranged as a linear array and only a segment of them is excited to a superradiant mode and emits light into the waveguide. Additional atomic chains placed on one or both sides play a passive role, either reflecting or absorbing this emission. We show that when varying the geo…
A trajectory approach is taken to the hydrodynamical treatment of collective excitations of a Bose-Einstein condensate in a harmonic trap. The excitations induced by linear deformations of the trap are shown to constitute a broad class of solutions that can be fully described by a simple nonlinear matrix equation. An exact closed-form expression is obtained for the solution describing the mode {n=0, m=2} in a cylindrically symmetric trap, and the calculated amplitude-dependent frequency shift shows good agreement with the experimental results of the JILA group.
Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here, we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform ef…
A superfluid atomic gas is prepared inside an optical resonator with an ultra-narrow band width on the order of the single photon recoil energy. When a monochromatic off-resonant laser beam irradiates the atoms, above a critical intensity the cavity emits superradiant light pulses with a duration on the order of its photon storage time. The atoms are collectively scattered into coherent superpositions of discrete momentum states, which can be precisely controlled by adjusting the cavity resonance frequency. With appropriate pulse sequences the entire atomic sample can be collectively accelerat…
Ultranarrow-linewidth atoms coupled to a lossy optical cavity mode synchronize, i.e. develop correlations, and exhibit steady-state superradiance when continuously repumped. This type of system displays rich collective physics and promises metrological applications. These features inspire us to investigate if analogous spin synchronization is possible in a different platform that is one of the most robust and controllable experimental testbeds currently available: ion-trap systems. We design a system with a primary and secondary species of ions that share a common set of normal modes of vibrat…
A hydrodynamic description is used to study the zero-temperature properties of a trapped spinor Bose-Einstein condensate in the presence of a uniform magnetic field. We show that, in the case of antiferromagnetic spin-spin interaction, the polar and ferromagnetic configurations of the ground state can coexist in the trap. These two phases are spatially segregated in such a way that the polar state occupies the inner part while the ferromagnetic state occupies the outer part of the atomic cloud. We also derive a set of coupled hydrodynamic equations for the number density and spin density excit…
