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Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are represented via an appropriately designed one-hot encoding of the constituent gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform the quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements., Comment: 17+ pages, 18 figures

In this paper, we propose an experimentally viable scheme to enhance the sensitivity of force detection in a hybrid optomechanical setup assisted by squeezed vacuum injection, beyond the standard quantum limit (SQL). The scheme is based on a combination of the coherent quantum noise cancellation (CQNC) strategy with a variational homodyne detection of the cavity output spectrum in which the phase of the local oscillator is optimized. In CQNC, realizing a negative-mass oscillator in the system leads to exact cancellation of the backaction noise from the mechanics due to destructive quantum interference. Squeezed vacuum injection enhances this cancellation and allows sub-SQL sensitivity to be reached in a wide frequency band and at much lower input laser powers. We show here that the adoption of variational homodyne readout enables us to enhance this noise cancellation up to $40 ~\mathrm{dB}$ compared to the standard case of detection of the optical output phase quadrature, leading to a remarkable force sensitivity of the order of $10^{-19} \mathrm{N}/\sqrt{\mathrm{Hz}}$, around 2-order enhancement compared to the standard case. Moreover, we show that at nonzero cavity detuning, the signal response can be amplified at a level three to five times larger than that in the standard case without variational homodyne readout, improving the signal-to-noise-ratio (SNR). Finally, the variational readout CQNC developed in this paper may be applied to other optomechanical-like platforms such as levitated systems and multimode optomechanical arrays or crystals as well as Josephson-based optomechanical systems., Comment: 18 pages; 18 figures

Quantum control techniques applied at macroscopic scales provide us with opportunities in fundamental physics and practical applications. Among them, measurement-based feedback allows efficient control of optomechanical systems and quantum-enhanced sensing. In this paper, we propose a near-resonant narrow-band force sensor with extremely low optically added noise in an optomechanical system subject to a feedback-controlled in-loop light. The membrane's intrinsic motion consisting of zero-point motion and thermal motion is affected by the added noise of measurement due to the backaction noise and imprecision noise. We show that, in the optimal low-noise regime, the system is analogous to an optomechanical system containing a near quantum-limited optical parametric amplifier coupled to an engineered reservoir interacting with the cavity. Therefore, the feedback loop enhances the mechanical response of the system to the input while keeping the optically added noise of measurement below the standard quantum limit. Moreover, the system based on feedback offers a much larger amplification bandwidth than the same system with no feedback.

Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that accounts for a minimal scale length, yield a dynamics that can be codified in additional Hamiltonian terms. When applied to the paradigmatic case of a mechanical oscillator, such terms, at the lowest order in the deformation parameter, introduce a weak intrinsic nonlinearity and, consequently, deviations from the classical trajectory. This point of view has stimulated several experimental proposals and realizations, leading to meaningful upper limits to the deformation parameter. All such experiments are based on classical mechanical oscillators, i.e., excited from a thermal state. We remark indeed that decoherence, that plays a major role in distinguishing the classical from the quantum behavior of (macroscopic) systems, is not usually included in phenomenological quantum gravity models. However, it would not be surprising if peculiar features that are predicted by considering the joined roles of gravity and quantum physics should manifest themselves just on purely quantum objects. On the base of this consideration, we propose experiments aiming to observe possible quantum gravity effects on macroscopic mechanical oscillators that are preliminary prepared in a high purity state, and we report on the status of their realization.

The theory of similarity for wind-driven seas is applied to the physical analysis of the problem of sea state bias (SSB) in altimetry measurements. Dimensionless wave steepness and pseudo-age derived from altimetry measurements are expected to provide {physically relevant and accurate enough} SSB estimates. Analysis of Jason-1,2,3 and SARAL/AltiKa data within the approach shows the similarity and robustness of SSB distributions re-casted onto space of wave pseudo-age and steepness. This result is considered as a ground for developing a new parametric model of SSB and for analysis of underlying physical effects.

Quantum illumination is a powerful sensing technique that employs entangled signal-idler photon pairs to boost the detection efficiency of low-reflectivity objects in environments with bright thermal noise. The promised advantage over classical strategies is particularly evident at low signal powers, a feature which could make the protocol an ideal prototype for non-invasive biomedical scanning or low-power short-range radar. In this work we experimentally investigate the concept of quantum illumination at microwave frequencies. We generate entangled fields using a Josephson parametric converter to illuminate a room-temperature object at a distance of 1 meter in a free-space detection setup. We implement a digital phase conjugate receiver based on linear quadrature measurements that outperforms a symmetric classical noise radar in the same conditions despite the entanglement-breaking signal path. Starting from experimental data, we also simulate the case of perfect idler photon number detection, which results in a quantum advantage compared to the relative classical benchmark. Our results highlight the opportunities and challenges on the way towards a first room-temperature application of microwave quantum circuits., Comment: 12 pages, 7 figures

The field of optomechanics provides us with several examples of quantum photon-phonon interface. In this paper, we theoretically investigate the generation and manipulation of quantum correlations in a microfabricated optomechanical array. We consider a system consisting of localized photonic and phononic modes interacting locally via radiation pressure at each lattice site with the possibility of hopping of photons and phonons between neighboring sites. We show that such an interaction can correlate various modes of a driven coupled optomechanical array with well-chosen system parameters. Moreover, in the linearized regime of Gaussian fluctuations, the quantum correlations not only survive in the presence of thermal noise, but may also be generated thermally. We find that these optomechanical arrays provide a suitable platform for quantum simulation of various many-body systems.

The sub-micron range in the field of short distance interactions has yet to be opened to experimental investigation, and may well hold the key to understanding al least part of the dark matter puzzle. The aKWISP (advanced-KWISP) project introduces the novel Double Membrane Interaction Monitor (DMIM), a combined source-sensing device where interaction distances can be as short as 100 nm or even 10 nm, much below the 1-10 micron distance which is the lower limit encountered by current experimental efforts. aKWISP builds on the technology and the results obtained with the KWISP opto-mechanical force sensor now searching at CAST for the direct coupling to matter of solar chameleons. It will reach the ultimate quantum-limited sensitivity by exploiting an array of technologies, including operation at milli-Kelvin temperatures. Recent suggestions point at short-distance interactions studies as intriguing possibilities for the detection of axions and of new physical phenomena., Comment: Submitted to the proceedings of "13Th Patras Workshop On Axions, Wimps And Wisps"

An opto--electro--mechanical system formed by a nanomembrane capacitively coupled to an LC resonator and to an optical interferometer has been recently employed for the high--sensitive optical readout of radio frequency (RF) signals [T. Bagci, \emph{et~al.}, Nature {\bf 507}, 81 (2013)]. Here we propose and experimentally demonstrate how the bandwidth of such kind of transducer can be increased by controlling the interference between two--electromechanical interaction pathways of a two--mode mechanical system. With a proof--of--principle device \new{operating at room temperature, we achieve a sensitivity of 300 nV/Hz^(1/2) over a bandwidth of 15 kHz in the presence of radiofrequency noise, and an optimal shot-noise limited sensitivity of 10 nV/Hz^(1/2) over a bandwidth of 5 kHz. We discuss strategies for improving the performance of the device, showing that, for the same given sensitivity, a mechanical multi--mode transducer can achieve a bandwidth} significantly larger than that of a single-mode one.

Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an appropriate definition of the phase difference operator for the resonators, we study synchronization in the quantum case through the covariance matrix formalism. We find that for sufficiently large driving, quantum synchronization is robust with respect to quantum fluctuations and to thermal noise up to not too large temperatures. Under synchronization, the two membranes are never entangled, while quantum discord behaves similarly to quantum synchronization, that is, it is larger when the variance of the phase difference is smaller.

We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of back-action noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broad-band detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise cancels exactly the back-action noise from the mechanical oscillator due to destructive quantum interference. Squeezed vacuum injection enforces this cancellation and allows to reach sub-SQL sensitivity in a very wide frequency band, and at much lower input laser powers., Comment: 13Pages, 5 Figures and 2 Appendix

We study the cavity mode frequencies of a Fabry-P\'erot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membranes are placed very close to a resonance of the inner cavity formed by them. We also study the cavity finesse of the system and verify that, under the conditions of large coupling, it is not appreciably affected by the presence of the two membranes. The achievable large values of the ratio between the optomechanical coupling and the cavity decay rate, $g/\kappa$, make this two-membrane system the simplest promising platform for implementing cavity optomechanics in the strong coupling regime., Comment: Contribution to the special issue on "Nano-optomechanics" in Journal of Optics, edited by I. Wilson-Rae, J. Sankey and H. Offerhaus

In view of the integration of membrane resonators with more complex MEMS structures, we developed a general fabrication procedure for circular shape SiN$_x$ membranes using Deep Reactive Ion Etching (DRIE). Large area and high-stress SiN$_x$ membranes were fabricated and used as optomechanical resonators in a Michelson interferometer and in a Fabry-P\'erot cavity. The measurements show that the fabrication process preserves both the optical quality and the mechanical quality factor of the membrane.

We investigate a general scheme for generating, either dynamically or in the steady state, continuous variable entanglement between two mechanical resonators with different frequencies. We employ an optomechanical system in which a single optical cavity mode driven by a suitably chosen two-tone field is coupled to the two resonators. Significantly large mechanical entanglement can be achieved, which is extremely robust with respect to temperature., Comment: To appear in New J. Phys. Small extensions in response to the points raised by the referee and Refs added

We propose a protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto-electro-mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may represent a fundamental tool for the realization of quantum networks connecting distant solid-state and superconducting qubits, which are typically manipulated with microwave fields. The certifying measurements on the optical modes guarantee the success of entanglement swapping without the need of performing explicit measurements on the distant microwave fields., Comment: 7 pages, 3 figures; to appear in the special issue "Quantum and Hybrid Mechanical Systems - From Fundamentals to Applications" in Annalen der Physik

Cavity optomechanical systems are approaching a strong-coupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the single-photon level which is experimentally feasible with state-of-the-art devices., Comment: 8 pages, 2 figures

We propose a scheme for the generation of a robust stationary squeezed state of a mechanical resonator in a quadratically coupled optomechanical system, driven by a pulsed laser. The intracavity photon number presents periodic intense peaks suddenly stiffening the effective harmonic potential felt by the mechanical resonator. These "optical spring kicks" tend to squeeze the resonator position, and due to the interplay with fluctuation-dissipation processes one can generate a stationary state with more than 13 dB of squeezing even starting from moderately "pre-cooled" initial thermal states., Comment: 5 pages, 3 figures. This paper supersedes an earlier version arXiv:1109.3905

Ponderomotive squeezing of the output light of an optical cavity has been recently observed in the MHz range in two different cavity optomechanical devices. Quadrature squeezing becomes particularly useful at lower spectral frequencies, for example in gravitational wave interferometers, despite being more sensitive to excess phase and frequency noise. Here we show a phase/frequency noise cancellation mechanism due to destructive interference which can facilitate the production of ponderomotive squeezing in the kHz range and we demonstrate it experimentally in an optomechanical system formed by a Fabry-P\'{e}rot cavity with a micro-mechanical mirror., Comment: 11 pages, 9 figures. Physical explanation expanded. Modified figures

We demonstrate the analogue of electromagnetically induced transparency in a room temperature cavity optomechanics setup formed by a thin semitransparent membrane within a Fabry-P\'erot cavity. Due to destructive interference, a weak probe field is completely reflected by the cavity when the pump beam is resonant with the motional red sideband of the cavity. Under this condition we infer a significant slowing down of light of hundreds of microseconds, which is easily tuned by shifting the membrane along the cavity axis. We also observe the associated phenomenon of electromagnetically induced amplification which occurs due to constructive interference when the pump is resonant with the blue sideband., Comment: 5 pages, 4 figures

We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of a thin semitransparent membrane placed within a high-finesse optical cavity. We study how the radiation pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor 350 We have also observed the mechanical frequency shift associated with the quadratic term in the expansion of the cavity mode frequency versus the effective membrane position, which is typically negligible in other cavity optomechanical devices., Comment: 15 pages, 7 figures

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 present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation treatment of the cavity eigenmodes., Comment: 10 pages, 6 figures

We describe a reversible quantum interface between an optical and a microwave field using a hybrid device based on their common interaction with a micro-mechanical resonator in a superconducting circuit. We show that, by employing state-of-the-art opto-electro-mechanical devices, one can realise an effective source of (bright) two-mode squeezing with an optical idler (signal) and a microwave signal, which can be used for high-fidelity transfer of quantum states between optical and microwave fields by means of continuous variable teleportation., Comment: 5 + 3 pages, 5 figures

We propose a scheme able to generate stationary continuous variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a micro-mechanical resonator. We show that when both cavities are intensely driven one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and opto-mechanical entanglement.

We show that optical spectroscopy of Rydberg states can provide accurate {\em in situ} thermometry at room-temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25 to 30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the Strontium clock transition. We demonstrate that magic wavelength lattices exist for both Strontium and Ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with $10^{-16}$ accuracy provide $10 \, \mathrm{mK}$ resolution and yield a blackbody uncertainty for the clock transition of $10^{-18}$.

We study the effect of laser phase noise on the generation of stationary entanglement between an intracavity optical mode and a mechanical resonator in a generic cavity optomechanical system. We show that one can realize robust stationary optomechanical entanglement even in the presence of non-negligible laser phase noise. We also show that the explicit form of the laser phase noise spectrum is relevant, and discuss its effect on both optomechanical entanglement and ground state cooling of the mechanical resonator., Comment: 13 pages, 9 figures

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 not pose serious limitations and that one can simultaneously achieve ground state cooling of a vibrational mode of the membrane and stationary optomechanical entanglement with state-of-the-art apparatuses., Comment: 14 pages, 7 figures

In the propagation of optical pulses through dispersive media, the frequency degree of freedom acts as an effective decohering environment on the polarization state of the pulse. Here we discuss the application of open-loop dynamical-decoupling techniques for suppressing such a polarization decoherence in one-way communication channels. We describe in detail the experimental proof of principle of the "bang-bang" protection technique recently applied to flying qubits in [Damodarakurup et al., Phys. Rev. Lett. 103, 040502]. Bang-bang operations are implemented through appropriately oriented waveplates and dynamical decoupling is shown to be potentially useful to contrast a generic decoherence acting on polarization qubits propagating in dispersive media like, e.g., optical fibers., Comment: 14 pages, 15 figures

Optomechanical systems are a promising candidate for the implementation of quantum interfaces for storing and redistributing quantum information. Here we focus on the case of a high-finesse optical cavity with a thin vibrating semitransparent membrane in the middle. We show that robust and stationary optomechanical entanglement could be achieved in the system, even in the presence of nonnegligible optical absorption in the membrane. We also present some preliminary experimental data showing radiation-pressure induced optical bistability., Comment: 6 pages, 2 figures. Work presented at the conference QCMC 2010 held on 19-23 July 2010 at the University of Queensland, Brisbane, Australia

We predict ground state cooling of a micro-mechanical oscillator, i.e. a vibrating end-mirror of an optical cavity, by resonant coupling of mirror vibrations to a narrow internal optical transition of an ensemble of two level systems. The particles represented by a collective mesoscopic spin model implement, together with the cavity, an efficient, frequency tailorable zero temperature loss channel which can be turned to a gain channel of pump. As opposed to the case of resolved-sideband cavity cooling requiring a small cavity linewidth, one can work here with low finesses and very small cavity volumes to enhance the light mirror and light atom coupling. The tailored loss and gain channels provide for efficient removal of vibrational quanta and suppress reheating. In a simple physical picture of sideband cooling, the atoms shape the cavity profile to enhance/inhibit scattering into higher/lower energy sidebands. The method should be applicable to other cavity based cooling schemes for atomic and molecular gases as for molecular ensembles coupled to stripline cavities.

The search for experimental demonstrations of the quantum behavior of macroscopic mechanical resonators is a fastly growing field of investigation and recent results suggest that the generation of quantum states of resonators with a mass at the microgram scale is within reach. In this chapter we give an overview of two important topics within this research field: cooling to the motional ground state, and the generation of entanglement involving mechanical, optical and atomic degrees of freedom. We focus on optomechanical systems where the resonator is coupled to one or more driven cavity modes by the radiation pressure interaction. We show that robust stationary entanglement between the mechanical resonator and the output fields of the cavity can be generated, and that this entanglement can be transferred to atomic ensembles placed within the cavity. These results show that optomechanical devices are interesting candidates for the realization of quantum memories and interfaces for continuous variable quantum communication networks., Comment: contribution chapter for Advances in Atomic, Molecular and Optical Physics, Volume 57, edited by Ennio Arimondo, Paul R. Berman and C. C. Lin

We perform an analysis of the optomechanical entanglement between the experimentally detectable output field of an optical cavity and a vibrating cavity end-mirror. We show that by a proper choice of the readout (mainly by a proper choice of detection bandwidth) one can not only detect the already predicted intracavity entanglement but also optimize and increase it. This entanglement is explained as being generated by a scattering process owing to which strong quantum correlations between the mirror and the optical Stokes sideband are created. All-optical entanglement between scattered sidebands is also predicted and it is shown that the mechanical resonator and the two sideband modes form a fully tripartite-entangled system capable of providing practicable and robust solutions for continuous variable quantum communication protocols.

We propose a scheme for the realization of a hybrid, strongly quantum-correlated system formed of an atomic ensemble surrounded by a high-finesse optical cavity with a vibrating mirror. We show that the steady state of the system shows tripartite and bipartite continuous variable entanglement in experimentally accessible parameter regimes, which is robust against temperature.

We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin., Comment: 6 pages, 3 figures

We describe a scheme showing signatures of macroscopic optomechanical entanglement generated by radiation pressure in a cavity system with a massive movable mirror. The system we consider reveals genuine multipartite entanglement. We highlight the way the entanglement involving the inaccessible massive object is unravelled, in our scheme, by means of field-field quantum correlations., Comment: 4 pages, 5 figure, RevTeX4

We show how stationary entanglement between an optical cavity field mode and a macroscopic vibrating mirror can be generated by means of radiation pressure. We also show how the generated optomechanical entanglement can be quantified and we suggest an experimental readout-scheme to fully characterize the entangled state. Surprisingly, such optomechanical entanglement is shown to persist for environment temperatures above 20K using state-of-the-art experimental parameters., Comment: 4 pages, 3 figures

The security of a deterministic quantum scheme for communication, namely the LM05 [1], is studied in presence of a lossy channel under the assumption of imperfect generation and detection of single photons. It is shown that the scheme allows for a rate of distillable secure bits higher than that pertaining to BB84 [2]. We report on a first implementation of LM05 with weak pulses., Comment: 10 pages, 3 figures. Uses OSID style

We analyze in detail the proposal for a two-qubit gate for travelling single-photon qubits recently presented by C. Ottaviani \emph{et al}. [Phys. Rev. A \textbf{73}, 010301(R) (2006)]. The scheme is based on an ensemble of five-level atoms coupled to two quantum and two classical light fields. The two quantum fields undergo cross-phase modulation induced by electromagnetically induced transparency. The performance of this two-qubit quantum phase gate for travelling single-photon qubits is thoroughly examined in the steady-state and transient regimes, by means of a full quantum treatment of the system dynamics. In the steady-state regime, we find a general trade-off between the size of the conditional phase shift and the fidelity of the gate operation. However, this trade-off can be bypassed in the transient regime, where a satisfactory gate operation is found to be possible, significantly reducing the gate operation time., Comment: 12 pages, 15 figures

In this work we bring together tools and ideology from two different fields, Symplectic Geometry and Asymptotic Geometric Analysis, to arrive at some new results. Our main result is a dimension-independent bound for the symplectic capacity of a convex body by its volume radius.

It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light., Comment: More information added

We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase modulation induced by electro-magnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for travelling single-photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation., Comment: 4 pages, 3 figures

A novel effect of population transfer in a five-level system is analyzed. This population transfer effect is found to be a version of a Raman process, which is facilitated and assisted by coherence effects, acting to close other available decay channels., Comment: International Wokshop and Seminar on Rydberg Physics, 19 April - 14 May 2004, Dresden, Germany

Large optical nonlinearities occurring in a coherently prepared atomic system are shown to produce phase shifts of order $\pi$. Such an effect may be observed in ultracold rubidium atoms where it could be feasibly exploited toward the realization of a polarization phase gate., Comment: Foundations of Quantum Information, Camerino, 16th-19th April 2004, Italy

We present the quantum theory of a polarization phase-gate that can be realized in a sample of ultracold rubidium atoms driven into a tripod configuration. The main advantages of this scheme are in its relative simplicity and inherent symmetry. It is shown that the conditional phase shifts of order $\pi$ can be attained., Comment: X International Conference on Quantum Optics, Minsk, Belarus

We show how a qubit can be fault-tolerantly encoded in the infinite-dimensional Hilbert space of an optical mode. The scheme is efficient and realizable with present technologies. In fact, it involves two travelling optical modes coupled by a cross-Kerr interaction, initially prepared in coherent states, one of which is much more intense than the other. At the exit of the Kerr medium, the weak mode is subject to a homodyne measurement and a quantum codeword is conditionally generated in the quantum fluctuations of the intense mode., Comment: 7 pages, 5 figures

We analyze the nonlinear optical response of a four-level atomic system driven into a tripod configuration. The large cross-Kerr nonlinearities that occurr in such a system are shown to produce nonlinear phase shift of order $\pi$. Such a substantial shift may be observed in a cold atomic gas in a magneto-optical trap where it coupl be fasibly exploited towards the realization of a polarization quantum phase gate. The experimental feasibility of such a gate is here examined in detail., Comment: Corrected version

We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation., Comment: 13 pages, 5 figures

We study the application of decoupling techniques to the case of a damped vibrational mode of a chain of trapped ions, which can be used as a quantum bus in linear ion trap quantum computers. We show that vibrational heating could be efficiently suppressed using appropriate ``parity kicks''. We also show that vibrational decoherence can be suppressed by this decoupling procedure, even though this is generally more difficult because the rate at which the parity kicks have to applied increases with the effective bath temperature., Comment: 13 pages, 5 figures. Typos corrected, references added

Recently it has been proposed to use parity as a measure of the mechanism behind decoherence or the transformation from quantum to classical. Here, we show that the proposed experiment is more feasible than previously thought, as even an initial thermal state would exhibit the hypothesized symmetry breaking., Comment: Proceedings of the Lake Garda "quantum puzzles" conference