Correlated excitations in a plane circular configuration of identical atoms with parallel dipole moments are investigated. The collective energy eigenstates, their level shifts and decay rates are computed utilizing a decomposition of the atomic state space into carrier spaces for the irreducible representations of the symmetry group $\ZZ_N$ of the circle. It is shown that the index $p$ of these representations can be used as a quantum number analogously to the orbital angular momentum quantum number $l$ in hydrogen-like systems. Just as the hydrogen s-states are the only electronic wave functions which can occupy the central region of the Coulomb potential, the quasi-particle corresponding to a collective excitation of the atoms in the circle can occupy the central atom only for vanishing $\ZZ_N$ quantum number $p$. If a central atom is present, the $p=0$ state splits into two and shows level-crossing at certain radii; in the regions between these radii, damped Rabi oscillations between two "extreme" $p=0$ configurations occur. The physical mechanisms behind super- and subradiance at a given radius and the divergence of the level shifts at small interatomic distances are discussed. It is shown that, beyond a certain critical number of atoms in the circle, the lifetime of the maximally subradiant state increases exponentially with the number of atoms in the configuration, making the system a natural candidate for a {\it single-photon trap}.
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 discuss three proposed schemes of initializing circular-state Rydberg atoms via optical couplings provided by the ponderomotive effect in contrast to the current circularization methods that utilize electric-dipole interactions. In our first proposed method, a radial optical trap consisting of two Laguerre-Gaussian beams of opposite winding numbers transfers orbital angular momentum to the Rydberg atom, providing a first-order coherent coupling between an F-state and a circular state. Additionally, we propose a one-dimensional ponderomotive optical lattice modulated at rf frequencies, provi…
When a single two-level atom interacts with a pair of Laguerre-Gaussian beams with opposite helicity, this leads to an efficient exchange of angular momentum between the light field and the atom. When the radial motion is trapped by an additional potential, the wave function of a single localized atom can be split into components that rotate in opposite direction. This suggests a novel scheme for atom interferometry without mirror pulses. Also atoms in this configuration can be bound into a circular lattice.
Rydberg atoms are remarkable tools for quantum simulation and computation. They are the focus of an intense experimental activity mainly based on low-angular-momentum Rydberg states. Unfortunately, atomic motion and levels lifetime limit the experimental time-scale to about 100$μ$s. Here, we demonstrate laser trapping of long-lived circular Rydberg states for up to 10ms. Our method is very general and opens many opportunities for quantum simulation. The 10ms trapping time corresponds to thousands of interaction cycles in a circular-state-based quantum simulator. It is also promising for quantu…
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 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.
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…
Abbreviated Abstract: We study correlated states in a circular and linear-chain configuration of identical two-level atoms containing the energy of a single quasi-resonant photon in the form of a collective excitation, where the collective behaviour is mediated by exchange of transverse photons between the atoms. For a circular configuration of atoms the effective Hamiltonian on the radiationless subspace of the system can be diagonalized analytically. In this case, the radiationless energy eigenstates carry a $\mathbb{Z}_N$ quantum number $p=0,1, ..., N$ which is analogous to the angular mome…
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.
We discuss a candidate solution for the controlled trapping and manipulation of two individual Rydberg atoms by means of a magnetic Ioffe-Pritchard trap that is superimposed by a constant electric field. In such a trap Rydberg atoms experience a permanent electric dipole moment that can be of the order of several hundred Debye. The interplay of electric dipolar repulsion and three dimensional magnetic confinement leads to a well controllable equilibrium configuration with tunable trap frequency and atomic distance. We thoroughly investigate the trapping potentials and analyze the interaction-i…
We investigate the collective excitations of a Raman-induced spin-orbit coupled Bose-Einstein condensate confined in a quasi one-dimension harmonic trap using the Bogoliubov method. By tuning the Raman coupling strength, three phases of the system can be identified. By calculating the transition strength, we are able to classify various excitation modes that are experimentally relevant. We show that the three quantum phases possess distinct features in their collective excitation properties. In particular, the spin dipole and the spin breathing modes can be used to clearly map out the phase bo…
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 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 study a simple model consisting of an atomic ion and a polar molecule trapped in a single setup, taking into consideration their electrostatic interaction. We determine analytically their collective modes of excitation as a function of their masses, trapping frequencies, distance, and the molecule's electric dipole moment. We then discuss the application of these collective excitations to cool molecules, to entangle molecules and ions, and to realize two-qubit gates between them. We finally present a numerical analysis of the possibility of applying these tools to study magnetically ordered…
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…
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…
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 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 …
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…
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…
We experimentally investigate $σ^+$-$σ^-$ polarization gradient cooling~(PGC) of a single $^{87}$Rb atom in a tightly focused dipole trap and show that the cooling limit strongly depends on the polarization of the trapping field. For optimized cooling light power, the temperature of the atom reaches~$10.4(6)\,μ$K in a linearly polarized trap, approximately five times lower than in a circularly polarized trap. The inhibition of PGC is qualitatively explained by the fictitious magnetic fields induced by the trapping field. We further demonstrate that switching the trap polarization from linear t…
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.
We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system's state ever exiting the protected subspace is provided.
Generating Einstein$\unicode{x2013}$Podolsky$\unicode{x2013}$Rosen correlations for teleporting collective spin states in a two dimensional trapped ion crystal
It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.
Universal ion trap computation on Decoherence Free Subspaces (DFS) using only two qubit operations is presented. The DFS is constructed for the collective dephasing model. Encoded single and two-qubit logical operations are implemented via the Sorensen-Molmer interaction. Alternation of the effective Hamiltonians for two particular phase configurations of control fields approximates an anisotropic exchange interaction. This is universal over suitable encodings of one logical qubit into three physical qubits which are also DFS under collective decoherence.
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…
We show that the quantum phase transition of the Tavis-Cummings model can be realised in a linear ion trap of the kind proposed for quantum computation. The Tavis-Cummings model describes the interaction between a bosonic degree of freedom and a collective spin. In an ion trap, the collective spin system is a symmetrised state of the internal electronic states of N ions, while the bosonic system is the vibrational degree of freedom of the centre of mass mode for the ions.
We present a technique, based on atoms coupled to an optical cavity, for non-destructive detection of trapped ions. We demonstrate the vacuum-Rabi splitting (VRS), arising due to the collective strong coupling of ultracold Rb atoms to a cavity, to change in presence of trapped Rb+ ions. The Rb+ ions are optically dark and the Rb atoms are prepared in a dark magneto-optical trap (MOT). The VRS is measured on an optically open transition of the initially dark Rb atoms. The measurement itself is fast, non-destructive and has sufficient fidelity to permit the measurement of atomic-state selective …
It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a non-linear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. This was achieved by usin…
