Mesoscopic Spin-Boson Models of Trapped Ions

Trapped ions arranged in Coulomb crystals provide us with the elements to study the physics of a single spin coupled to a boson bath. In this work we show that optical forces allow us to realize a variety of spin-boson models, depending on the crystal geometry and the laser configuration. We study in detail the Ohmic case, which can be implemented by illuminating a single ion with a travelling wave. The mesoscopic character of the phonon bath in trapped ions induces new effects like the appearance of quantum revivals in the spin evolution.Comment: 4.4 pages, 5 figure

Coupled multimode optomechanics in the microwave regime

The motion of micro- and nanomechanical resonators can be coupled to electromagnetic fields. This allows to explore the mutual interaction and introduces new means to manipulate and control both light and mechanical motion. Such optomechanical systems have recently been implemented in nanoelectromechanical systems involving a nanomechanical beam coupled to a superconducting microwave resonator. Here, we propose optomechanical systems that involve multiple, coupled microwave resonators. In contrast to similar systems in the optical realm, the coupling frequency governing photon exchange between microwave modes is naturally comparable to typical mechanical frequencies. For instance this enables new ways to manipulate the microwave field, such as mechanically driving coherent photon dynamics between different modes. In particular we investigate two setups where the electromagnetic field is coupled either linearly or quadratically to the displacement of a nanomechanical beam. The latter scheme allows to perform QND Fock state detection. For experimentally realistic parameters we predict the possibility to measure an individual quantum jump from the mechanical ground state to the first excited state.Comment: 6 pages, 4 figures, 1 tabl

Spin Relaxation in a Quantum Dot due to Nyquist Noise

We calculate electron and nuclear spin relaxation rates in a quantum dot due to the combined action of Nyquist noise and electron-nuclei hyperfine or spin-orbit interactions. The relaxation rate is linear in the resistance of the gate circuit and, in the case of spin-orbit interaction, it depends essentially on the orientations of both the static magnetic field and the fluctuating electric field, as well as on the ratio between Rashba and Dresselhaus interaction constants. We provide numerical estimates of the relaxation rate for typical system parameters, compare our results with other, previously discussed mechanisms, and show that the Nyquist mechanism can have an appreciable effect for experimentally relevant systems.Comment: v2: New discussion of arbitrary gate setups (1 new figure), more Comments on experiments; 6 pages, 4 figure

Full photon statistics of a light beam transmitted through an optomechanical system

In this paper, we study the full statistics of photons transmitted through an optical cavity coupled to nanomechanical motion. We analyze the entire temporal evolution of the photon correlations, the Fano factor, and the effects of strong laser driving, all of which show pronounced features connected to the mechanical backaction. In the regime of single-photon strong coupling, this allows us to predict a transition from sub-Poissonian to super-Poissonian statistics for larger observation time intervals. Furthermore, we predict cascades of transmitted photons triggered by multi-photon transitions. In this regime, we observe Fano factors that are drastically enhanced due to the mechanical motion.Comment: 8 pages, 7 figure

Decoherence of a particle in a ring

We consider a particle coupled to a dissipative environment and derive a perturbative formula for the dephasing rate based on the purity of the reduced probability matrix. We apply this formula to the problem of a particle on a ring, that interacts with a dirty metal environment. At low but finite temperatures we find a dephasing rate $\propto T^{3/2}$, and identify dephasing lengths for large and for small rings. These findings shed light on recent Monte Carlo data regarding the effective mass of the particle. At zero temperature we find that spatial fluctuations suppress the possibility of having a power law decay of coherence.Comment: 5 pages, 1 figure, proofed version to be published in EP

Electron-nuclei spin relaxation through phonon-assisted hyperfine interaction in a quantum dot

We investigate the inelastic spin-flip rate for electrons in a quantum dot due to their contact hyperfine interaction with lattice nuclei. In contrast to other works, we obtain a spin-phonon coupling term from this interaction by taking directly into account the motion of nuclei in the vibrating lattice. In the calculation of the transition rate the interference of first and second orders of perturbation theory turns out to be essential. It leads to a suppression of relaxation at long phonon wavelengths, when the confining potential moves together with the nuclei embedded in the lattice. At higher frequencies (or for a fixed confining potential), the zero-temperature rate is proportional to the frequency of the emitted phonon. We address both the transition between Zeeman sublevels of a single electron ground state as well as the triplet-singlet transition, and we provide numerical estimates for realistic system parameters. The mechanism turns out to be less efficient than electron-nuclei spin relaxation involving piezoelectric electron-phonon coupling in a GaAs quantum dot.Comment: 8 pages, 1 figur

Naturally-phasematched second harmonic generation in a whispering gallery mode resonator

We demonstrate for the first time natural phase matching for optical frequency doubling in a high-Q whispering gallery mode resonator made of Lithium Niobate. A conversion efficiency of 9% is achieved at 30 micro Watt in-coupled continuous wave pump power. The observed saturation pump power of 3.2 mW is almost two orders of magnitude lower than the state-of-the-art. This suggests an application of our frequency doubler as a source of non-classical light requiring only a low-power pump, which easily can be quantum noise limited. Our theoretical analysis of the three-wave mixing in a whispering gallery mode resonator provides the relative conversion efficiencies for frequency doubling in various modes