Introduction to Quantum Noise, Measurement and Amplification

The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and AMO/quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, we describe the basics of weak continuous measurements. Particular attention is given to treating the standard quantum limit on linear amplifiers and position detectors using a general linear-response framework. We show how this approach relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics, and illustrate its application for the case of electrical circuits, including mesoscopic detectors and resonant cavity detectors.Comment: Substantial improvements over initial version; include supplemental appendices

Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion

We present a fully quantum theory describing the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the opto-mechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.Comment: 5 pages, 2 figure

Dynamical multistability in high-finesse micromechanical optical cavities

We analyze the nonlinear dynamics of a high-finesse optical cavity in which one mirror is mounted on a flexible mechanical element. We find that this system is governed by an array of dynamical attractors, which arise from phase-locking between the mechanical oscillations of the mirror and the ringing of the light intensity in the cavity. We describe an analytical approximation to map out the diagram of attractors in parameter space, derive the slow amplitude dynamics of the system, including thermally activated hopping between different attractors, and suggest a scheme for exploiting the dynamical multistability in the measurement of small displacements.Comment: 5 pages, 4 figure

The information about the state of a qubit gained by a weakly coupled detector

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.Comment: 21 pages (two column), 8 figure

Radiation-pressure self-cooling of a micromirror in a cryogenic environment

We demonstrate radiation-pressure cavity-cooling of a mechanical mode of a micromirror starting from cryogenic temperatures. To achieve that, a high-finesse Fabry-Perot cavity (F\approx 2200) was actively stabilized inside a continuous-flow 4He cryostat. We observed optical cooling of the fundamental mode of a 50mu x 50 mu x 5.4 mu singly-clamped micromirror at \omega_m=3.5 MHz from 35 K to approx. 290 mK. This corresponds to a thermal occupation factor of \approx 1x10^4. The cooling performance is only limited by the mechanical quality and by the optical finesse of the system. Heating effects, e.g. due to absorption of photons in the micromirror, could not be observed. These results represent a next step towards cavity-cooling a mechanical oscillator into its quantum ground state

Application of Resonance Perturbation Theory to Dynamics of Magnetization in Spin Systems Interacting with Local and Collective Bosonic Reservoirs

We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions for the evolution of the reduced density matrix elements. This allows us to calculate explicitly the dynamics of the macroscopic magnetization, including characteristic relaxation and dephasing time-scales. We demonstrate that collective effects (i) do not influence the character of the relaxation processes but merely renormalize the relaxation times, and (ii) significantly modify the dephasing times, leading in some cases to a complicated (time inhomogeneous) dynamics of the transverse magnetization, governed by an effective time-dependent magnetic field

Cavity cooling of a nanomechanical resonator by light scattering

We present a novel method for opto-mechanical cooling of sub-wavelength sized nanomechanical resonators. Our scheme uses a high finesse Fabry-Perot cavity of small mode volume, within which the nanoresonator is acting as a position-dependant perturbation by scattering. In return, the back-action induced by the cavity affects the nanoresonator dynamics and can cool its fluctuations. We investigate such cavity cooling by scattering for a nanorod structure and predict that ground-state cooling is within reach.Comment: 4 pages, 3 figure

Quantum nano-electromechanics with electrons, quasiparticles and Cooper pairs: effective bath descriptions and strong feedback effects

Using a quantum noise approach, we discuss the physics of both normal metal and superconducting single electron transistors (SET) coupled to mechanical resonators. Particular attention is paid to the regime where transport occurs via incoherent Cooper-pair tunneling (either via the Josephson quasiparticle (JQP) or double Josephson quasiparticle (DJQP) process). We show that, surprisingly, the back-action of tunneling Cooper pairs (or superconducting quasiparticles) can be used to significantly cool the oscillator. We also discuss the physical origin of negative damping effects in this system, and how they can lead to a regime of strong electro-mechanical feedback, where despite a weak SET - oscillator coupling, the motion of the oscillator strongly effects the tunneling of the Cooper pairs. We show that in this regime, the oscillator is characterized by an energy-dependent effective temperature. Finally, we discuss the strong analogy between back-action effects of incoherent Cooper-pair tunneling and ponderomotive effects in an optical cavity with a moveable mirror; in our case, tunneling Cooper pairs play the role of the cavity photons.Comment: 27 pages, 7 figures; submitted to the New Journal of Physics focus issue on Nano-electromechanical Systems; error in references correcte

Circuit Quantum Electrodynamics: Coherent Coupling of a Single Photon to a Cooper Pair Box

Under appropriate conditions, superconducting electronic circuits behave quantum mechanically, with properties that can be designed and controlled at will. We have realized an experiment in which a superconducting two-level system, playing the role of an artificial atom, is strongly coupled to a single photon stored in an on-chip cavity. We show that the atom-photon coupling in this circuit can be made strong enough for coherent effects to dominate over dissipation, even in a solid state environment. This new regime of matter light interaction in a circuit can be exploited for quantum information processing and quantum communication. It may also lead to new approaches for single photon generation and detection.Comment: 8 pages, 4 figures, accepted for publication in Nature, embargo does apply, version with high resolution figures available at: http://www.eng.yale.edu/rslab/Andreas/content/science/PubsPapers.htm

Phase preserving amplification near the quantum limit with a Josephson Ring Modulator

Recent progress in solid state quantum information processing has stimulated the search for ultra-low-noise amplifiers and frequency converters in the microwave frequency range, which could attain the ultimate limit imposed by quantum mechanics. In this article, we report the first realization of an intrinsically phase-preserving, non-degenerate superconducting parametric amplifier, a so far missing component. It is based on the Josephson ring modulator, which consists of four junctions in a Wheatstone bridge configuration. The device symmetry greatly enhances the purity of the amplification process and simplifies both its operation and analysis. The measured characteristics of the amplifier in terms of gain and bandwidth are in good agreement with analytical predictions. Using a newly developed noise source, we also show that our device operates within a factor of three of the quantum limit. This development opens new applications in the area of quantum analog signal processing