We investigate theoretically the mechanical effects of light on atoms trapped by an external potential, whose dipole transition couples to the mode of an optical resonator and is driven by a laser. We derive an analytical expression for the quantum center-of-mass dynamics, which is valid in presence of a tight external potential. This equation has broad validity and allows for a transparent interpretation of the individual scattering processes leading to cooling. We show that the dynamics are a competition of the mechanical effects of the cavity and of the laser photons, which may mutually interfere. We focus onto the good-cavity limit and identify novel cooling schemes, which are based on quantum interference effects and lead to efficient ground state cooling in experimentally accessible parameter regimes.
An optical lattice with rubidium atoms ($^{85}Rb$) is formed inside a ring resonator with a finesse of $1.8 \times 10^5$ and a large mode volume of 1.3 $mm^3$. We typically trap several times $10^6$ atoms at densities up to $10^{12} cm^{-3}$ and temperatures between 25 and 125 $μK$. Despite of the narrow bandwidth (17.3 kHz) of the cavity, heating due to intra--cavity intensity fluctuations is kept at a low level, such that the time evolution of the temperature is determined by evaporative cooling.
We experimentally investigate the interaction between one and two atoms and the field of a high-finesse optical resonator. Laser-cooled caesium atoms are transported into the cavity using an optical dipole trap. We monitor the interaction dynamics of a single atom strongly coupled to the resonator mode for several hundred milliseconds by observing the cavity transmission. Moreover, we investigate the position-dependent coupling of one and two atoms by shuttling them through the cavity mode. We demonstrate an alternative method, which suppresses heating effects, to analyze the atom-field intera…
We have built a microwave Fabry-Perot resonator made of diamond-machined copper mirrors coated with superconducting niobium. Its damping time (Tc = 130 ms at 51 GHz and 0.8 K) corresponds to a finesse of 4.6 x 109, the highest ever reached for a Fabry-Perot in any frequency range. This result opens novel perspectives for quantum information, decoherence and non-locality studies.
We predict that the collective excitations of an atomic array become entangled with the light of a high-finesse cavity mode when they are suitably coupled. This entanglement is of Einstein-Podolsky-Rosen type, it is robust against cavity losses and is a stationary property of the coupled system. It is generated when the atomic array is aligned along the cavity axis and driven transversally by a laser, when coherent scattering of photons into the cavity mode is suppressed because of phase-mismatching. We identify the parameter regimes under which entanglement is found and show that these are co…
We present a novel microfabricated optical cavity, which combines a very small mode volume with high finesse. In contrast to other micro-resonators, such as microspheres, the structure we have built gives atoms and molecules direct access to the high-intensity part of the field mode, enabling them to interact strongly with photons in the cavity for the purposes of detection and quantum-coherent manipulation. Light couples directly in and out of the resonator through an optical fibre, avoiding the need for sensitive coupling optics. This renders the cavity particularly attractive as a component…
We study the spectra of emission of a system composed by an atom, tightly confined inside a high-finesse resonator, when the atom is driven by a laser and is at steady state of the cooling dynamics induced by laser and cavity field. In general, the spectrum of resonance fluorescence and the spectrum at the cavity output contain complementary information about the dynamics undergone by the system. In certain parameter regimes, quantum interference effects between the scattering processes induced by cavity and laser field lead to the selective suppression of features of the resonance fluorescenc…
Cavity-enhanced radiation-pressure coupling of optical and mechanical degrees of freedom gives rise to a range of optomechanical phenomena, in particular providing a route to the quantum regime of mesoscopic mechanical oscillators. A prime challenge in cavity optomechanics has however been to realize systems which simultaneously maximize optical finesse and mechanical quality. Here we demonstrate for the first time independent control over both mechanical and optical degree of freedom within one and the same on-chip resonator. The first direct observation of mechanical normal mode coupling in …
We describe a fiber ring resonator comprised of a relatively long loop of standard single-mode fiber with a short nanofiber segment. The evanescent mode of the nanofiber segment allows the cavity-enhanced field to interact with atoms in close proximity to the nanofiber surface. We report on an experiment using a warm atomic vapor and low-finesse cavity, and briefly discuss the potential for reaching the strong coupling regime of cavity QED by using trapped atoms and a high-finesse cavity of this kind.
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…
The quadrupole S$_{1/2}$ -- D$_{5/2}$ optical transition of a single trapped Ca$^+$ ion, well suited for encoding a quantum bit of information, is coherently coupled to the standing wave field of a high finesse cavity. The coupling is verified by observing the ion's response to both spatial and temporal variations of the intracavity field. We also achieve deterministic coupling of the cavity mode to the ion's vibrational state by selectively exciting vibrational state-changing transitions and by controlling the position of the ion in the standing wave field with nanometer-precision.
We show that a low finesse cavity can be efficient for detecting neutral atoms. The low finesse can be compensated for by decreasing the mode waist of the cavity. We have used a near concentric resonator with a beam waist of 12$μ$m and a finesse of only 1100 to detect magnetically guided Rb atoms with a detection sensitivity of 0.1 atom in the mode volume. For future experiments on single atom detection and cavity QED applications, it should be very beneficial to use miniaturized optical resonator integrated on atom chips.
We have fabricated an atom chip device which combines the circuitry for magnetic trapping of cold atoms with high-finesse optical resonators suitable for cavity QED in the single-atom strong coupling regime. Fabry-Perot optical resonators with finesse F > 2 X 10^5 were formed between a micropatterned on-chip planar mirror with lateral dimension of < 100 um and a curved mirror suspended above the chip. The strong and rapid thermal coupling between on-chip electrical and optical elements was utilized to stabilize the cavity mirror separation with servo bandwidth exceeding 100 kHz during simulate…
We derive an equation for the cooling dynamics of the quantum motion of an atom trapped by an external potential inside an optical resonator. This equation has broad validity and allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. Our result shows that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.
We experimentally demonstrate the high-sensitivity optical monitoring of a micro-mechanical resonator and its cooling by active control. Coating a low-loss mirror upon the resonator, we have built an optomechanical sensor based on a very high-finesse cavity (30000). We have measured the thermal noise of the resonator with a quantum-limited sensitivity at the 10^-19 m/rootHz level, and cooled the resonator down to 5K by a cold-damping technique. Applications of our setup range from quantum optics experiments to the experimental demonstration of the quantum ground state of a macroscopic mechanic…
The radiation pressure coupling between a low-mass moving mirror and an incident light field has been experimentally studied in a high-finesse Fabry-Perot cavity. Using classical intensity noise in order to mimic radiation pressure quantum fluctuations, the physics of ponderomotive squeezing comes into play as a result of the opto-mechanical correlations between the field quadratures. The same scheme can be used to probe ponderomotive squeezing at the quantum level, thus opening new routes in quantum optics and high sensitivity measurement experiments.
We calculate explicitly the space dependence of the radiative relaxation rates and associated level shifts for a dipole placed in the vicinity of the center of a spherical cavity with a large numerical aperture and a relatively low finesse. In particular, we give simple and useful analytic formulas for these quantities, that can be used with arbitrary mirrors transmissions. The vacuum field in the vicinity of the center of the cavity is actually equivalent to the one obtained in a microcavity, and this scheme allows one to predict significant cavity QED effects.
We describe an experiment in which a laser beam is sent into a high-finesse optical cavity with a mirror coated on a mechanical resonator. We show that the reflected light is very sensitive to small mirror displacements. We have observed the Brownian motion of the resonator with a very high sensitivity.
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…
An experiment is performed where a single rubidium atom trapped within a high-finesse optical cavity emits two independently triggered entangled photons. The entanglement is mediated by the atom and is characterized both by a Bell inequality violation of S=2.5, as well as full quantum-state tomography, resulting in a fidelity exceeding F=90%. The combination of cavity-QED and trapped atom techniques makes our protocol inherently deterministic - an essential step for the generation of scalable entanglement between the nodes of a distributed quantum network.
Optical resonators are increasingly important tools in science and technology. Their applications range from laser physics, atomic clocks, molecular spectroscopy, and single-photon generation to the detection, trapping and cooling of atoms or nano-scale objects. Many of these applications benefit from strong mode confinement and high optical quality factors, making small mirrors of high surface-quality desirable. Building such devices in silicon yields ultra-low absorption at telecom wavelengths and enables integration of micro-structures with mechanical, electrical and other functionalities. …
The transmission spectrum for one atom strongly coupled to the field of a high-finesse optical resonator is observed to exhibit a clearly resolved vacuum-Rabi splitting characteristic of the normal modes in the eigenvalue spectrum of the atom-cavity system. A new Raman scheme for cooling atomic motion along the cavity axis enables a complete spectrum to be recorded for an individual atom trapped within the cavity mode, in contrast to all previous measurements in cavity QED that have required averaging over many atoms.
Optical microcavities allow to strongly confine light in small mode volumes and with long photon lifetimes. This confinement significantly enhances the interaction between light and matter inside the cavity, with applications such as optical trapping and cooling of nanoparticles, single-photon emission enhancement, quantum information processing, and sensing. For many applications, open resonators with direct access to the mode volume are necessary. Here we report on a scalable, open-access optical microcavity platform with mode volumes < 30 $λ^3$ and finesse approaching $5x10^5$. This result …
The inherent coupling of optical and mechanical modes in high finesse optical microresonators provide a natural, highly sensitive transduction mechanism for micromechanical vibrations. Using homodyne and polarization spectroscopy techniques, we achieve shot-noise limited displacement sensitivities of 10^(-19) m Hz^(-1/2). In an unprecedented manner, this enables the detection and study of a variety of mechanical modes, which are identified as radial breathing, flexural and torsional modes using 3-dimensional finite element modelling. Furthermore, a broadband equivalent displacement noise is me…
We demonstrate the reversible mapping of a coherent state of light with mean photon number n-bar ~= 1.1 to and from the hyperfine states of an atom trapped within the mode of a high finesse optical cavity. The coherence of the basic processes is verified by mapping the atomic state back onto a field state in a way that depends on the phase of the original coherent state. Our experiment represents an important step towards the realization of cavity QED-based quantum networks, wherein coherent transfer of quantum states enables the distribution of quantum information across the network.
A novel approach to optics integration in ion traps is demonstrated based on a surface electrode ion trap that is microfabricated on top of a dielectric mirror. Additional optical losses due to fabrication are found to be as low as 80 ppm for light at 422 nm. The integrated mirror is used to demonstrate light collection from, and imaging of, a single 88 Sr+ ion trapped $169\pm4 μ$m above the mirror.
We show that a single, trapped, laser-driven atom in a high-finesse optical cavity allows for the quantum-coherent generation of entangled light pulses on demand. Schemes for generating simultaneous and temporally separated pulse pairs are proposed. The mechanical effect of the laser excitation on the quantum motion of the cold trapped atom mediates the entangling interaction between two cavity modes and between the two subsequent pulses, respectively. The entanglement is of EPR-type, and its degree can be controlled through external parameters. At the end of the generation process the atom is…
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.
Trapping ions in Paul traps requires high radio-frequency voltages, which are generated using resonators. When operating traps in a cryogenic environment, an in-vacuum resonator showing low loss is crucial to limit the thermal load to the cryostat. In this study, we present a guide for the design and production of compact, shielded cryogenic resonators. We produced and characterized three different types of resonators and furthermore demonstrate efficient impedance matching of these resonators at cryogenic temperatures.
Coherent control of the spatial properties of light is central to a wide variety of applications from high bandwidth quantum and classical communication to high power fiber lasers. Low-loss conversion amongst a complete and orthogonal set of modes is particularly important for robust mode-multiplexed communication. Here, we introduce tunable impedance mismatch between coupled Fabry-Pérot resonators as a powerful tool for manipulation of the spatial and temporal properties of optical fields. In the single-mode regime, frequency dependent impedance matching enables tunable finesse optical resona…
We study the dynamics of a supersonic molecular beam in a low-finesse optical cavity and demonstrate that most molecules in the beam can be decelerated to zero central velocity by the intracavity optical field in a process analogous to electrostatic Stark deceleration. We show that the rapid switching of the optical field for slowing the molecules is automatically generated by the cavity-induced dynamics. We further show that $\sim1\%$ of the molecules can be optically trapped at a few millikelvin in the same cavity.
We propose a tunable phonon laser prototype with a large trapped ion array, where some of the ions are effectively pinned by optical tweezers, thus isolating a subset of ions that mimics an acoustic cavity used as a phonon lasing resonator. The cavity loss can then be controlled by the tweezer strength and the "wall thickness", the number of pinned ions for isolation. We pump the resonator by applying blue-sideband lasers, and investigate the lasing dynamics of the cavity modes such as threshold behavior, population distribution, the second-order coherence, and line-narrowed spectrum. This sch…
We study the quantum effects of radiation pressure in a high-finesse cavity with a mirror coated on a mechanical resonator. We show that the optomechanical coupling can be described by an effective susceptibility which takes into account every acoustic modes of the resonator and their coupling to the light. At low frequency this effective response is similar to a harmonic response with an effective mass smaller than the total mass of the mirror. For a plano-convex resonator the effective mass is related to the light spot size and becomes very small for small optical waists, thus enhancing the …
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict, in particular, that for high cooperativi…
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications, where they typically require precise stabilization of their optical resonances. Here, we study two different approaches to construct fiber Fabry-Perot resonators and stabilize their length for experiments in cavity quantum electrodynamics with neutral atoms. A piezo-mechanically actuated cavity with feedback based on the Pound-Drever-Hall locking technique is compared to a novel rigid cavity design that makes use of the hig…
The topic of this thesis is the theoretical analysis of the optomechanical coupling effects in a high-finesse optical cavity, and the experimental realization of such a device. Radiation pressure exerted by light limits the sensitivity of high precision optical measurements. In particular, the sensitivity of interferometric measurements of gravitational wave is limited by the so called standard quantum limit. cavity with a movable mirror. The internal field stored in such cavity can be orders of magnitude greater than the input field, and it's radiation pressure force can change the physical l…
We propose a scheme for entangling the optical and microwave output modes of the respective cavities by using a micro mechanical resonator. The micro-mechanical resonator on one side is capacitively coupled to the microwave cavity and on the other side is coupled to a high finesses optical cavity. We then show how this continuous variable entanglement can be profitably used to teleport the non-Gaussian number state |1> and the superposition (|0>+|1>)/\surd2 from the microwave cavity output mode onto an output of optical cavity mode with fidelity much larger than the no-cloning limit.
We demonstrate passive feedback cooling of a mechanical resonator based on radiation pressure forces and assisted by photothermal forces in a high-finesse optical cavity. The resonator is a free-standing high-reflectance micro-mirror (of mass m=400ng and mechanical quality factor Q=10^4) that is used as back-mirror in a detuned Fabry-Perot cavity of optical finesse F=500. We observe an increased damping in the dynamics of the mechanical oscillator by a factor of 30 and a corresponding cooling of the oscillator modes below 10 K starting from room temperature. This effect is an important ingredi…
Light scattering by a periodic atomic array is studied when the atoms couple with the mode of a high-finesse optical resonator and are driven by a laser. When the von-Laue condition is not satified, there is no coherent emission into the cavity mode, and the latter is pumped via inelastic scattering processes. We consider this situation and identify conditions for which different non-linear optical processes can occur. We show that these processes can be controlled by suitably tuning the strength of laser and cavity coupling, the angle between laser and cavity axis, and the array periodicity. …
We show theoretically that two atomic dipoles in a resonator constitute a non-linear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics could be observed as a result of self-organization of laser-cooled atoms in resonators.
We first consider the basic requirements for a quantum computer, arguing for the attractiveness of nuclear spins as information-bearing entities, and light for the coupling which allows quantum gates. We then survey the strengths of and immediate prospects for quantum information processing in ion traps. We discuss decoherence and gate rates in ion traps, comparing methods based on the vibrational motion with a method based on exchange of photons in cavity QED. We then sketch the main features of a quantum computer designed to allow an algorithm needing 10^6 Toffoli gates on 100 logical qubits…
We study the entangling power of a nanoelectromechanical system (NEMS) simultaneously interacting with two separately trapped ions. To highlight this entangling capability, we consider a special regime where the ion-ion coupling does not generate entanglement in the system, and any resulting entanglement will be the result of the NEMS acting as an entangling device. We study the dynamical behavior of the bipartite NEMS-induced ion-ion entanglement as well as the tripartite entanglement of the whole system (ions+NEMS). We found some quite remarkable phenomena in this hybrid system. For instance…
Optomechanical devices in which a flexible SiN membrane is placed inside an optical cavity allow for very high finesse and mechanical quality factor in a single device. They also provide fundamentally new functionality: the cavity detuning can be a quadratic function of membrane position. This enables a measurement of "position squared" ($x^2$) and in principle a QND phonon number readout of the membrane. However, the readout achieved using a single transverse cavity mode is not sensitive enough to observe quantum jumps between phonon Fock states. Here we demonstrate an $x^2$-sensitivity that …
The efficiency of cavity sideband cooling of trapped molecules is theoretically investigated for the case where the IR transition between two rovibrational states is used as a cycling transition. The molecules are assumed to be trapped either by a radio-frequency or optical trapping potential, depending on whether they are charged or neutral, and confined inside a high-finesse optical resonator which enhances radiative emission into the cavity mode. Using realistic experimental parameters and COS as a representative molecular example, we show that in this setup cooling to the trap ground state…
We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We first derive the general multimode Hamiltonian describing the radiation pressure interaction between the cavity modes and the vibrational modes of the membrane. We then restrict the analysis to the standard case of a single cavity mode interacting with a single mechanical resonator and we determine to what extent optical absorption by the membrane hinder reaching a quantum regime for the cavity-membrane system. We show that membrane absorption does n…
We experimentally realize an optical fiber ring resonator that includes a tapered section with subwavelength-diameter waist. In this section, the guided light exhibits a significant evanescent field which allows for efficient interfacing with optical emitters. A commercial tunable fiber beam splitter provides simple and robust coupling to the resonator. Key parameters of the resonator such as its out-coupling rate, free spectral range, and birefringence can be adjusted. Thanks to the low taper- and coupling-losses, the resonator exhibits an unloaded finesse of F=75+/-1, sufficient for reaching…
Two major challenges in the development of optomechanical devices are achieving a low mechanical and optical loss rate and vibration isolation from the environment. We address both issues by fabricating trampoline resonators made from low pressure chemical vapor deposition (LPCVD) Si$_3$N$_4$ with a distributed bragg reflector (DBR) mirror. We design a nested double resonator structure with 80 dB of mechanical isolation from the mounting surface at the inner resonator frequency, and we demonstrate up to 45 dB of isolation at lower frequencies in agreement with the design. We reliably fabricate…
We analyze the performance of a quantum repeater protocol based on single trapped ions. At each node, single trapped ions embedded into high finesse cavities emit single photons whose polarization is entangled with the ion state. A specific detection of two photons at a central station located half-way between two nodes heralds the entanglement of two remote ions. Entanglement can be extended to long distances by applying successive entanglement swapping operations based on two-ion gate operations that have already been demonstrated experimentally with high precision. Our calculation shows tha…
We prepare and detect the hyperfine state of a single 87Rb atom coupled to a fiber-based high finesse cavity on an atom chip. The atom is extracted from a Bose-Einstein condensate and trapped at the maximum of the cavity field, resulting in a reproducibly strong atom-cavity coupling. We use the cavity reflection and transmission signal to infer the atomic hyperfine state with a fidelity exceeding 99.92% in a read-out time of 100 microseconds. The atom is still trapped after detection.
We present exact numerical solutions of the damped-driven Jaynes--Cummings model adapted to describe absorptive optical bistability in the limit of a few atoms strongly coupled to a high-finesse resonator. We show that the simplifying semiclassical result for many physical quantities of interest is well reproduced by the quantum model including even with only a few atoms in the strongly coupled system. Nontrivial atom-field quantum cross-correlations show up in the strong-driving limit.
An electron floating on the liquid Helium is proposed to be trapped (by a micro-electrode set below the liquid Helium) in a high finesse cavity. Two lowest levels of the vertical motion of the electron acts as a two-level "atom", which could resonantly interact with the THz cavity. In the Lamb-Dicke regime, wherein the electron's in-plane activity region is much smaller than the wavelength of the cavity mode, the famous Jaynes-Cummings model (JCM) could be realized. By applying an additional external classical laser beam to the electron, a driven JCM could also be implemented. With such a driv…
We analyze the dynamics of a chain of singly-charged ions confined in a linear Paul trap and which couple with the mode of a high-finesse optical resonator. In these settings the ions interact via the Coulomb repulsion and are subject to the mechanical forces due to scattering of cavity photons. We show that the interplay of these interactions can give rise to bistable equilibrium configurations, into which the chain can be cooled by cavity-enhanced photon scattering. We characterize the resulting equilibrium structures by determining the stationary state in the semiclassical limit for both ca…
Cavity-based quantum node is a competitive platform for distributed quantum networks. Here, we characterize a high-finesse Fabry-Perot optical resonator for coupling single or few atomic quantum registers. Our cavity consists of two mirrors with different reflectivities: One has minimal optical loss, and the other high transmission loss where more than 90% of the intracavity photons would be emitted. Cavity finesse, birefringent effects, and mechanical resonances are measured using the lasers at 780, 782, and 795 nm. In order to obtain cavity geometric parameters, we drive the adjacent longitu…
We propose a scheme to unconditionally entangle the internal states of atoms trapped in separate high finesse optical cavities. The scheme uses the technique of quantum reservoir engineering in a cascaded cavity QED setting, and for ideal (lossless) coupling between the cavities generates an entangled pure state. Highly entangled states are also shown to be possible for realizable cavity QED parameters and with nonideal coupling.
