Quantum Measurement Theory in Gravitational-Wave Detectors

The fast progress in improving the sensitivity of the gravitational-wave (GW) detectors, we all have witnessed in the recent years, has propelled the scientific community to the point, when quantum behaviour of such immense measurement devices as kilometer-long interferometers starts to matter. The time, when their sensitivity will be mainly limited by the quantum noise of light is round the corner, and finding the ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of Standard Quantum Limit and the methods of its surmounting.Comment: 147 pages, 46 figures, 1 table. Published in Living Reviews in Relativit

Quantum Zeno effect and the detection of gravitomagnetism

In this work we introduce two experimental proposals that could shed some light upon the inertial properties of intrinsic spin. In particular we will analyze the role that the gravitomagnetic field of the Earth could have on a quantum system with spin 1/2. We will deduce the expression for Rabi transitions, which depend, explicitly, on the coupling between the spin of the quantum system and the gravitomagnetic field of the Earth. Afterwards, the continuous measurement of the energy of the spin 1/2 system is considered, and an expression for the emerging quantum Zeno effect is obtained. Thus, it will be proved that gravitomagnetism, in connection with spin 1/2 systems, could induce not only Rabi transitions but also a quantum Zeno effect.Comment: Essay awarded with an ``honorable mention'' in the Annual Essay Competition of the Gravity Research Foundation for the year 2000, four new references, discussion enlarged, 9 pages. Accepted in International Journal of Modern Physics

Resolved Sideband Cooling of a Micromechanical Oscillator

Micro- and nanoscale opto-mechanical systems provide radiation pressure coupling of optical and mechanical degree of freedom and are actively pursued for their ability to explore quantum mechanical phenomena of macroscopic objects. Many of these investigations require preparation of the mechanical system in or close to its quantum ground state. Remarkable progress in ground state cooling has been achieved for trapped ions and atoms confined in optical lattices. Imperative to this progress has been the technique of resolved sideband cooling, which allows overcoming the inherent temperature limit of Doppler cooling and necessitates a harmonic trapping frequency which exceeds the atomic species' transition rate. The recent advent of cavity back-action cooling of mechanical oscillators by radiation pressure has followed a similar path with Doppler-type cooling being demonstrated, but lacking inherently the ability to attain ground state cooling as recently predicted. Here we demonstrate for the first time resolved sideband cooling of a mechanical oscillator. By pumping the first lower sideband of an optical microcavity, whose decay rate is more than twenty times smaller than the eigen-frequency of the associated mechanical oscillator, cooling rates above 1.5 MHz are attained. Direct spectroscopy of the motional sidebands reveals 40-fold suppression of motional increasing processes, which could enable reaching phonon occupancies well below unity (<0.03). Elemental demonstration of resolved sideband cooling as reported here should find widespread use in opto-mechanical cooling experiments. Apart from ground state cooling, this regime allows realization of motion measurement with an accuracy exceeding the standard quantum limit.Comment: 13 pages, 5 figure

Cooling a nanomechanical resonator with quantum back-action

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radiofrequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position;back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550mK to 300mK-- an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these backaction effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.Comment: 28 pages, 7 figures; accepted for publication in Natur

Sideband Cooling Micromechanical Motion to the Quantum Ground State

The advent of laser cooling techniques revolutionized the study of many atomic-scale systems. This has fueled progress towards quantum computers by preparing trapped ions in their motional ground state, and generating new states of matter by achieving Bose-Einstein condensation of atomic vapors. Analogous cooling techniques provide a general and flexible method for preparing macroscopic objects in their motional ground state, bringing the powerful technology of micromechanics into the quantum regime. Cavity opto- or electro-mechanical systems achieve sideband cooling through the strong interaction between light and motion. However, entering the quantum regime, less than a single quantum of motion, has been elusive because sideband cooling has not sufficiently overwhelmed the coupling of mechanical systems to their hot environments. Here, we demonstrate sideband cooling of the motion of a micromechanical oscillator to the quantum ground state. Entering the quantum regime requires a large electromechanical interaction, which is achieved by embedding a micromechanical membrane into a superconducting microwave resonant circuit. In order to verify the cooling of the membrane motion into the quantum regime, we perform a near quantum-limited measurement of the microwave field, resolving this motion a factor of 5.1 from the Heisenberg limit. Furthermore, our device exhibits strong-coupling allowing coherent exchange of microwave photons and mechanical phonons. Simultaneously achieving strong coupling, ground state preparation and efficient measurement sets the stage for rapid advances in the control and detection of non-classical states of motion, possibly even testing quantum theory itself in the unexplored region of larger size and mass.Comment: 13 pages, 7 figure

Sub-Planck spots of Schroedinger cats and quantum decoherence

Heisenberg's principle$^1$ states that the product of uncertainties of position and momentum should be no less than Planck's constant $\hbar$. This is usually taken to imply that phase space structures associated with sub-Planck ($\ll \hbar$) scales do not exist, or, at the very least, that they do not matter. I show that this deeply ingrained prejudice is false: Non-local "Schr\"odinger cat" states of quantum systems confined to phase space volume characterized by `the classical action' $A \gg \hbar$ develop spotty structure on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Such structures arise especially quickly in quantum versions of classically chaotic systems (such as gases, modelled by chaotic scattering of molecules), that are driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum manifestations of the exponential sensitivity to perturbations$^2$. Most importantly, these sub-Planck scales are physically significant: $a$ determines sensitivity of a quantum system (or of a quantum environment) to perturbations. Therefore sub-Planck $a$ controls the effectiveness of decoherence and einselection caused by the environment$^{3-8}$. It may also be relevant in setting limits on sensitivity of Schr\"odinger cats used as detectors.Comment: Published in Nature 412, 712-717 (2001

Quantum non-demolition measurement of a superconducting two-level system

In quantum mechanics, the process of measurement is a subtle interplay between extraction of information and disturbance of the state of the quantum system. A quantum non-demolition (QND) measurement minimizes this disturbance by using a particular system - detector interaction which preserves the eigenstates of a suitable operator of the quantum system. This leads to an ideal projective measurement. We present experiments in which we perform two consecutive measurements on a quantum two -level system, a superconducting flux qubit, by probing the hysteretic behaviour of a coupled nonlinear resonator. The large correlation between the results of the two measurements demonstrates the QND nature of the readout method. The fact that a QND measurement is possible for superconducting qubits strengthens the notion that these fabricated mesoscopic systems are to be regarded as fundamental quantum objects. Our results are also relevant for quantum information processing, where projective measurements are used for protocols like state preparation and error correction.Comment: 14 pages, 4 figure

Are Interaction-free Measurements Interaction Free?

In 1993 Elitzur and Vaidman introduced the concept of interaction-free measurements which allowed finding objects without ``touching'' them. In the proposed method, since the objects were not touched even by photons, thus, the interaction-free measurements can be called as ``seeing in the dark''. Since then several experiments have been successfully performed and various modifications were suggested. Recently, however, the validity of the term ``interaction-free'' has been questioned. The criticism of the name is briefly reviewed and the meaning of the interaction-free measurements is clarified.Comment: 11 pages, 3 eps figures. Contribution to the ICQO 2000, Raubichi, Belaru

Quantum jumps of light recording the birth and death of a photon in a cavity

A microscopic system under continuous observation exhibits at random times sudden jumps between its states. The detection of this essential quantum feature requires a quantum non-demolition (QND) measurement repeated many times during the system evolution. Quantum jumps of trapped massive particles (electrons, ions or molecules) have been observed, which is not the case of the jumps of light quanta. Usual photodetectors absorb light and are thus unable to detect the same photon twice. They must be replaced by a transparent counter 'seeing' photons without destroying them3. Moreover, the light has to be stored over a duration much longer than the QND detection time. We have fulfilled these challenging conditions and observed photon number quantum jumps. Microwave photons are stored in a superconducting cavity for times in the second range. They are repeatedly probed by a stream of non-absorbing atoms. An atom interferometer measures the atomic dipole phase shift induced by the non-resonant cavity field, so that the final atom state reveals directly the presence of a single photon in the cavity. Sequences of hundreds of atoms highly correlated in the same state, are interrupted by sudden state-switchings. These telegraphic signals record, for the first time, the birth, life and death of individual photons. Applying a similar QND procedure to mesoscopic fields with tens of photons opens new perspectives for the exploration of the quantum to classical boundary

Radiation-pressure cooling and optomechanical instability of a micro-mirror

Recent experimental progress in table-top experiments or gravitational-wave interferometers has enlightened the unique displacement sensitivity offered by optical interferometry. As the mirrors move in response to radiation pressure, higher power operation, though crucial for further sensitivity enhancement, will however increase quantum effects of radiation pressure, or even jeopardize the stable operation of the detuned cavities proposed for next-generation interferometers. The appearance of such optomechanical instabilities is the result of the nonlinear interplay between the motion of the mirrors and the optical field dynamics. In a detuned cavity indeed, the displacements of the mirror are coupled to intensity fluctuations, which modifies the effective dynamics of the mirror. Such "optical spring" effects have already been demonstrated on the mechanical damping of an electromagnetic waveguide with a moving wall, on the resonance frequency of a specially designed flexure oscillator, and through the optomechanical instability of a silica micro-toroidal resonator. We present here an experiment where a micro-mechanical resonator is used as a mirror in a very high-finesse optical cavity and its displacements monitored with an unprecedented sensitivity. By detuning the cavity, we have observed a drastic cooling of the micro-resonator by intracavity radiation pressure, down to an effective temperature of 10 K. We have also obtained an efficient heating for an opposite detuning, up to the observation of a radiation-pressure induced instability of the resonator. Further experimental progress and cryogenic operation may lead to the experimental observation of the quantum ground state of a mechanical resonator, either by passive or active cooling techniques