We have realized a fiber-based Fabry-Perot cavity with CO 2 lasermachined mirrors. It combines very small size, high finesse F ≥ 130000, small waist and mode volume, and good mode matching between the fiber and cavity modes. This combination of features is a major advance for cavity quantum electrodynamics (CQED), as shown in recent CQED experiments with Bose-Einstein condensates enabled by this cavity [Y. Colombe et al., Nature 450, 272 (2007)]. It should also be suitable for a wide range of other applications, including coupling to solid-state emitters, gas detection at the single-particle level, fiber-coupled single-photon sources and high-resolution optical filters with large stopband.

When two resonant modes in a system with gain or loss coalesce in both their resonance position and their width, a so-called exceptional point occurs, which acts as a source of non-trivial physics in a diverse range of systems. Lasers provide a natural setting to study such non-Hermitian degeneracies, as they feature resonant modes and a gain material as their basic constituents. Here we show that exceptional points can be conveniently induced in a photonic molecule laser by a suitable variation of the applied pump. Using a pair of coupled microdisk quantum cascade lasers, we demonstrate that in the vicinity of these exceptional points the coupled laser shows a characteristic reversal of its pump dependence, including a strongly decreasing intensity of the emitted laser light for increasing pump power.

We perform Ramsey spectroscopy on the ground state of ultra-cold 87 Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 ± 12 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and may appear in other physical systems.In atomic clocks and other precision techniques based on atomic spin manipulation [1], a central requirement is to preserve the coherence of a state superposition over long times. Understanding how coherence decays in a given system is important for these applications, and is a touchstone of understanding its dynamics. In trapped ensembles, an inhomogeneous shift ∆(r) of the transition frequency occurs due to the trapping potential and to atomic interactions. Different atoms explore different regions of this shift landscape, and so their spins precess at different rates. This leads to dephasing at a rate determined by the characteristic inhomogeneity ∆ 0 of ∆(r) over the ensemble. Various mechanisms have been exploited to reduce this dephasing. Examples are "magic fields" that strongly reduce the field dependence for a specific transition [2,3], or the mutual compensation scheme successfully employed in ultracold 87 Rb [4], where the trap-induced inhomogeneity can be adjusted to nearly cancel the collisional mean-field inhomogeneity. All such mechanisms however, including the motional narrowing well known in nuclear magnetic resonance, have in common that the dephasing is merely slowed down, but never reversed, and the transverse polarization remains a steadily decreasing function of time.Here we present measurements on a trapped ensemble of 87 Rb atoms with two internal levels equivalent to a spin 1/2. Atomic interactions cause a spontaneous re-phasing of the spins, observed as a much longer decay time and revivals of Ramsey contrast. We are also able to extend the coherence time by more than an order of magnitude beyond the 2 to 3 s previously achieved on this system [3,5]. We explain these remarkable results by a very general mechanism based on the identical spin rotation effect (ISRE) that occurs during collisions in the forward direction between two identical particles [6] -an equivalent description can be given in terms of the exchange mean-field experienced by the atoms [7]. This effect is known to cause transient spin waves [4,[8][9][10][11][12][13][14], a deleterious phenomenon if one is interested in long coherence times. In contrast to those experiments however, we are working in a regime where both (i) the ISRE rate (exchange rate) ω ex /2π = 2 |a 01 |n/m is FIG. 1: Two classes of atoms (red and blue) precess at different rates. Their Bloch vectors were initially parallel, but have started to...

In this paper we study a system consisting of two nearly degenerate mechanical modes that couple to a single mode of an optical cavity. We show that this coupling leads to nearly complete (99.5%) hybridization of the two mechanical modes into a bright mode that experiences strong optomechanical interactions and a dark mode that experiences almost no optomechanical interactions. We use this hybridization to transfer energy between the mechanical modes with 40% efficiency.PACS numbers: 42.50. Wk, 42.81.Wg, 42.60.Da, 85.85.+j, Optomechanical systems, in which electromagnetic resonators interact with mechanical resonators, offer a platform for studying a wide range of nonlinear and quantum effects. These systems have been studied in the context of quantum-limited detection of forces and displacements, the production of nonclassical states of light, synchronization and chaotic dynamics, and tests of quantum mechanics with massive degrees of freedom. [1] Optomechanical systems are usually modeled as a single optical mode that is parametrically coupled to a single mechanical mode. This simple model accurately describes many experiments; however, real devices invariably consist of multiple optical and mechanical modes. The presence of multiple modes can provide important capabilities, including new types of optomechanical interactions, robust means for detecting quantum effects, and the ability to transfer quantum states between different systems. [2][3][4][5][6][7][8][9][10][11][12][13] One important class of multimode optomechanical systems consists of devices in which a single optical mode couples to multiple mechanical modes. This situation arises naturally when an optomechanical device with wellseparated optical resonances is driven by a single laser beam. Within the usual weak-coupling description of optomechanics the undriven optical modes are irrelevant, and only the driven mode needs to be considered. [14][15][16] Mechanical modes, on the other hand, cannot be ignored just because they are not driven. This is because any optical mode can be detuned (to some degree) by the displacement of any of the devices' mechanical modes. As a result the effective Hamiltonian for such a device will involve one optical mode coupled to many mechanical modes.In such a system, the motion of a given mechanical mode will modulate the intracavity optical field, which will in turn drive the other mechanical modes. This can be thought of as an optically mediated coupling between the mechanical modes. This intermode coupling can be neglected for mechanical modes whose resonance frequencies are well separated. However, mechanical resonators with * alexey.shkarin@yale.edu some degree of symmetry will have some nearly degenerate modes, and for these modes this coupling can be important.In this paper we demonstrate that the optomechanical coupling between one optical mode and two mechanical modes causes the mechanical modes to nearly fully (99.5%) hybridize into bright and dark states. We then transfer classical mechanical energy betwee...

We report on the coupling of a single nitrogen-vacancy (NV) center in a nanodiamond to a fiber-based microcavity at room temperature. Investigating the very same NV center inside the cavity and in free space allows us to systematically explore a regime of phonon-assisted cavity feeding. Making use of the NV center's strongly broadened emission, we realize a widely tunable, narrow band single photon source. A master equation model well reproduces our experimental results and predicts a transition into a Purcell-enhanced emission regime at low temperatures.

We analyze theoretically several crucial performance aspects of terahertz quantum cascade lasers, such as the impact of doping on the threshold current, the relative importance of the various scattering mechanisms, and the balance of coherent transport and realistic energy dissipation. We have developed a fully self-consistent model for stationary charge transport based on nonequilibrium Green's function theory that takes into account incoherent scattering with phonons, impurities, and rough interfaces as well as electron-electron scattering in the Hartree approximation, but does not a priori assume the electron distributions to follow the periodicity of the quantum cascade laser ͑QCL͒ structure. The theoretical results show excellent quantitative agreement with experimental data. We find scattering at rough interfaces to strongly affect electronic transport and efficiently limit the optical gain. Our results also indicate that a large portion of the current is maintained by coherent multibarrier tunneling. We show that this dominant coherent transport may lead to electron distributions that do not follow the periodicity of the QCL.

We describe an optomechanical device consisting of a fiber-based optical cavity containing a silicon nitiride membrane. In comparison with typical free-space cavities, the fiber-cavity's small mode size (10 µm waist, 80 µm length) allows the use of smaller, lighter membranes and increases the cavity-membrane linear coupling to 3 GHz/nm and the quadratic coupling to 20 GHz/nm 2 . This device is also intrinsically fiber-coupled and uses glass ferrules for passive alignment. These improvements will greatly simplify the use of optomechanical systems, particularly in cryogenic settings. At room temperature, we expect these devices to be able to detect the shot noise of radiation pressure.In quantum mechanics, a measurement of one variable is accompanied by back-action on the conjugate variable. In the particular case of an optical displacement measurement, the quantum back-action is radiation pressure shot noise (RPSN) 1,2 , the Poissonian noise in the momentum transferred by reflecting photons.When a high-finesse cavity is used to increase the sensitivity of the displacement measurement, the RPSN is also increased. The connection between increased cavity finesse, increased measurement sensitivity, and increased RPSN can be understood qualitatively by noting that the number of times each photon interacts with a mechanical element inside a cavity is approximately equal to the cavity finesse.In the field of optomechanics, floppy mechanical elements are integrated into high-finesse optical cavities in order to observe various quantum effects, including RPSN 3,4 . The goal of observing RPSN is motivated by basic questions about quantum measurements, as well as by the fact that RPSN is expected to limit the performance of next-generation gravitational-wave observatories (though squeezed light can be used to mitigate the effect) 5,6 . To date, RPSN has not been observed in solid-state optomechanical devices, largely because it has been obscured by the thermal Langevin force that produces Brownian motion 7 . While it has been proposed that correlation measurements can be used to distinguish RPSN in the presence of a much larger Langevin force 7,8 , such a measurement would be simplified by increasing the RPSN relative to the thermal Langevin force. There is an additional motivation for increasing the RPSN: the optomechanical generation of squeezed light (e.g. for improving the performance of gravitational-wave observatories) requires a setup in which the RPSN dominates over the Langevin force 9,10 . Increasing the effect of RPSN in comparison to thermal motion involves optimizing both the mechanical system a) Electronic mail: nathan.flowers-jacobs@yale.edu = 82 A 2n /κ when the laser is resonant with the cavity and the mechanical resonance frequency ω m is much less than the cavity FWHM linewidth κ (the "bad cavity" limit). Thus, the RPSN force is increased by increasing the optomechanical coupling A = dω cav /dx, increasing the average number of photons stored in the cavityn, and decreasing κ.In this paper, we present a n...

We present the realization of a combined trapped-ion and optical cavity system, in which a single Yb + ion is confined by a micron-scale ion trap inside a 230 µm-long optical fiber cavity. We characterize the spatial ion-cavity coupling and measure the ion-cavity coupling strength using a cavity-stimulated Λ-transition. Owing to the small mode volume of the fiber resonator, the coherent coupling strength between the ion and a single photon exceeds the natural decay rate of the dipole moment. This system can be integrated into ion-photon quantum networks and is a step towards cavity quantum-electrodynamics (cavity-QED) based quantum information processing with trapped ions.Trapped atomic ions play an important role in studies of small, isolated quantum systems, for example in quantum information processing and precision metrology. Aside from the long achievable coherence times, their success is largely based on the excellent manipulation and interrogation possibilities of their internal quantum states, which are usually performed by optical means. In order to employ the outstanding properties of trapped ions for future applications such as cavity-QED based quantum computers [1] or quantum network nodes [2][3][4], strong coupling between a single ion and a single photon is a prerequisite, i.e., the coherent coupling strength must exceed the decoherence rate of the atomic dipole moment. Unlike for neutral atoms [5,6] and solid-state emitters, such as quantum dots [7] or Cooper pairs [8], this strong coupling regime has not yet been reached for a single trapped ion despite decade-long efforts [9][10][11][12][13][14][15].The route to achieve strong light-matter coupling employs the principles of cavity-QED; a resonator changes the mode structure of the vacuum electromagnetic field in order to strongly enhance coupling to one photon mode. The coupling strength g between a single emitter and a single-photon mode depends on the mode-volume V of the cavity and on the electric dipole moment d of the transition, g ∝ d/ √ V . Owing to the large mode volumes of the cavities used in previous experiments [9][10][11][12][13][14][15], the coherent single-photon coupling rate g has been inferior to the decay rate Γ of the atomic dipole moment. The main restriction has been that the crucial ingredient to achieve strong coupling, namely placing the ion near dielectric mirror surfaces which are necessary to form an optical cavity, has been found to severely compromise the performance of a Paul trap [16]. For sizing down both the mode-volume and the amount of dielectric material, the development of cavities based on optical fibers [17] has opened a new perspective, also with respect to the integration of optical elements into microchip-based ion traps. Optical fiber cavities offer significantly smaller radii of curvature of the mirrors, which lead to a small waist of the field mode inside the optical cavity. Recently, significant experimental efforts have been devoted to integrating optical fibers with ion traps for efficient light c...