We revisit the scheme of singlephoton weakcoupling optomechanics using postselection, proposed by pepper, ghobadi, jeffrey, simon, and bouwmeester phys. The scheme is realizable for sufficiently strong singlephoton optomechanical coupling in the resolved sideband regime, and. In the mechanical rotating frame with the conjugate quadratures. Cavity optomechanics with a boseeinstein condensate science. Quantum phases are quantum states of matter at zero temperature. The field of quantum cavity optomechanics, which focuses on the mutual interaction between an optical cavity field and the motion of a mechanical object via. Paritytimesymmetric quantum critical phenomena nature. Bochove department of physics, texas tech university, lubbock, texas 79409 richard j. Getting to zero quantum effects in any system are most pronounced when the influence of thermal fluctuations can be ignored.
Towards optomechanical quantum state reconstruction of. The phase space distribution fx, p of a quantum state is a quasiprobability distribution. Broadly speaking, quantum optomechanics provides a universal tool to achieve the quantum control of mechanical motion 1. By pairing optical or microwave cavi ties with mechanical resonators to form a cavity opto mechanical system, one acquires a means to achieve quantum control over mechanical motion or, conversely, mechanical control over optical or. Chapter 3 gives comprehensive discussion of the quantum limit on the added noise of a continuous position detector, following the quantum linear response approach. Optomechanics may provide the most e cient way of converting quantum information at ghzfrequencies. This translates into a phase shift of the reflectedtransmitted light beam, which can be used to read out the mechanical motion. Here we study the phase acquired by a radiation field after its radiation pressure interaction with a mechanical oscillator, and compare the classical and quantum contributions.
The dynamics of the direct and phaseconjugate modes exhibit familiar timereversed qualities, leading to opposite sign temperatures for the modes in the classical regime of operation. Interactiontermswithderivativeswouldalsoarisebystartingfromthemicroscopictheory,translatingfrom kspaceintorealspace. This project lies at the boundary between two fields that have witnessed extraordinary progress in the last few years. In the second half of my talk, i will discuss our ideas to realize tunable optical delay lines, quantum memories for light, and singlephoton nonlinearities using optomechanical systems. Open thermal management and nonreciprocal control of. Quantum synchronization of chaotic oscillator behaviors among coupled becoptomechanical systems springerlink. Without loss of generality, we may choose the phases of. Quantum optomechanics beyond the quantum coherent oscillation. The noncommutativity of canonical conjugate operators can induce phases on quantum systems, which. The dynamics of the direct and phase conjugate modes exhibit familiar timereversed qualities, leading to opposite sign temperatures. The physics is just that of a system of two linearly coupled harmonic oscillators, albeit one with a great deal of tunability, and one where the dissipative rates and e ective temperatures of the two oscillators can be very di erent. He institute for lasers, photonics and biophotonics, state university of new york at buffalo. As this technique is feasible for use in many significant applications, the study of opc has become one of the most active research subjects in the areas of nonlinear optics and quantum electronics.
As a physical parameter is varied, quantum fluctuations can drive a phase transition into a different phase of matter. Here the authors show that in a strongly correlated many. The notes then focus on selected topics relating to quantum measurement and quantum optomechanics. In the phase space formulation, the phase space distribution may be treated as the fundamental, primitive description of the quantum system, without any reference to wave functions or density matrices. They also consider the impact of quantum optomechanics on tests of gravitational physics. Andersen1 1department of physics, technical university of denmark, building 309, 2800 kongens lyngby, denmark 2australian research council centre of excellence for engineered quantum systems equs, school of mathematics and. The first is ultracold atomic science and the second is quantum optomechanics, this latter area. By pairing optical or microwave cavities with mechanical resonators to form a cavity opto mechanical system, one acquires a means to achieve quantum control over mechanical motion or, conversely, mechanical control over optical or.
B characterization of laser phase noise in semiconductor diode lasers. First, the operation of silicon optomechanical crystals in the quantum. Pdf probability density function, p 112 povm positiveoperator valued measure, p 64 qle quantum langevin equation, p 15. While many approaches exist, they typically share a simple effective description in terms of a single force acting on the mechanical resonator. It does that in devices spanning a vast range of parameters, with mechanical frequencies from a few hertz to ghz, and with masses from 10. Research in the group involves theoretical and experimental exploration of new platforms for higher dimensional nonlinear optics and their associated technological applications. Their major research achievements in nonlinear optics include the pioneering studies of twowavecoupled refractiveindex change, ramanenhanced selffocusing, opticalfrequency pockels effect, stimulated kerr scattering, optical phase conjugation via backward stimulated emission, and twophotonabsorption based optical limiting, stabilization. Brillouin scattering is a nonlinear optical effect involving the interaction of. Blanter kavli institute of nanoscience, delft university of technology standard quantum limit and quantum detection quantum state transfer nonlinearity and radiation pressure nonlinear cavity. Classic holography involves a reference beam and an object beam which bounces off an object which interact and form a holographic interference pattern on a holographic plate grating.
Quantum optomechanics beyond the quantum coherent oscillation regime kiran khosla 1. Optomechanics in fiber and microstructured waveguides. While much of this discussion can already be found in clerk, 2004. Pdf the control of quantum systems requires the ability to change and readout the phase of a system. So, ideally, a mechanical quantum experiment would start with the mechanical element in its quantum ground state of motion, in. Pdf oscillatorfield model of moving mirrors in quantum. Phase conjugation is a physical transformation of a wave field where the resulting field has a reversed propagation direction but keeps its amplitudes and phases. Quantum theory of spontaneous emission and excitation near a phase conjugating mirror peter w.
Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on lowenergy scales. Quantum theory of continuum optomechanics iopscience. Positive and negative amplification effects of the displacement of the mirrors position can be generated when. Boyd abstract we show that it is possible to control with good accuracy the relative phase of several conjugate. We report on a cavity optomechanical system in which a collective density excitation of a boseeinstein condensate serves as the mechanical oscillator coupled to the cavity field. Introduction to optomechanics klemens hammerer imprs lecture week mardorf 19 centre for quantum engineering and spacetime research leibniz university hannover institute for theoretical physics institute for gravitational physics aei. We present a quantum electrodynamic theory of spontaneous emission i11 the presence of a phase conjugating. We address the quantum classical comparison of phase measurements in optomechanics in the general framework of berry phases for composite systems. The receiver transforms the returning microwave field to the optical domain while performing a phase conjugate operation.
For the small couplings characteristic of optomechanics 3, we can neglect the interactions quadratic in. Quantum gravity, gravitational frequency spectrum, mass oscillator synchronization, spectral energy density modulation and phase conjugation. Hybrid cavity quantum electrodynamics optomechanics. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks. The past decade witnessed a breathtakingly fast progress in the area of quantum optomechanics. Cavity quantum optomechanics is now one of the most exciting and fervent areas of modern quantum physics and embodies a viable route towards mesoscopic quantumness and the exploration of the quantum toclassical transition. In quantum electrodynamics the interpretation of phase conjugation is much simpler compared to classical electrodynamics.
Electromagnetically induced transparency and slow light with optomechanics, nature. For a fixed cavity drive frequency, the reflection phase shift. Bowen 1center for engineered quantum systems, university of queensland, st lucia 4072, australia and. Paritytime pt symmetry has been mainly studied in optical and weakly interacting open quantum systems without manybody correlations. Even at zero temperature a quantum mechanical system has quantum fluctuations and therefore can still support phase transitions. Measurementinduced macroscopic superposition states in. These ultrahighq modes should open up a viable route to quantum optomechanics even in roomtemperature environments. Quantum science and technology, volume 4, number 2, april. These features are limited by quantum effects due to the noncommutative nature of quantummechanical operators. So far, experimental research, especially in the quantum regime, has focused on canonical systems with only one optical and mechanical degree of freedomor mode, respectively.
When the interaction is sufficiently strong, such that more than one thermal phonon is introduced within a period of oscillation, quantum coherent oscillations are prevented. Milburn is a professor of physics at the university of queensland and director of the australian research council centre of excellence for engineered quantum systems. Pdf we present a microphysics model for the kinematics and dynamics. Journal of optics, volume 18, number 8, august 2016 iopscience. Recently, the quantum mechanical character of this interaction has been of particular interest.
Osa quantum optomechanics beyond the quantum coherent. Other readers will always be interested in your opinion of the books youve read. We consider and theoretically analyze a boseeinstein condensate bec trapped inside an optomechanical system consisting of singlemode optical cavity with a moving end mirror. Cavity optomechanics with a nonlinear photoniccrystal. His current research interests include quantum optomechanics, precision metrology and sensing, and biological applications of quantum measurement. This is generally thought to preclude a wide range of quantum protocols. Brendel c, schmidt m and marquardt f 2015 topological phases of sound and light phys. Quantum wave mechanics by larry reed order the complete book from the publisher. Quantum synchronization of chaotic oscillator behaviors. Hybrid cavity optomechanics provides an alternative approach by coupling mechanical objects to quantum emitters, either directly or indirectly via the common interaction with a cavity field mode. Phase space formulation of quantum mechanics tony bracken centre for mathematical physics and department of mathematics university of queensland smft07, melbourne, januaryfebruary 2007. Optomechanics is the field of research studying the interaction of light and mechanical motion of mesoscopic objects. Multimode optomechanical system in the quantum regime pnas.
Only relative phases are meaningful in quantum mechanics. Measurementinduced macroscopic superposition states in cavity optomechanics ulrich b. They explain how an alternative form of a hybrid optomechanical system leads to the phenomenon of synchronization. Phase locking via brillouinenhanced fourwavemixing. Search and pierre meystre, phase conjugation of a quantum degenerate atomic fermi beam, phys. Article thermal management and nonreciprocal control of phonon.
Quantum theory of spontaneous emission and excitation near. The bec is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Optomechanics and quantum measurement aashish clerk. Quantum synchronization of chaotic oscillator behaviors among. Phase conjugation in quantum optomechanics university of. The complex conjugate of a complex number z is denoted by z. It is a cross field of optics, quantum optics, solidstate physics and materials science. Interaction with a thermal environment decoheres the quantum state of a mechanical oscillator. We analyze the phase conjugate coupling of a pair of optomechanical oscillator modes driven by the timedependent beatnote due to a twocolor optical field. When applied on the onedimensional hubbard, xy spin chain with threespin interaction, and suschriefferheeger.
Phase conjugation is of interest in a variety of applications in which. However, the ensuing fundamental limits on the measurement sensitivity of gravimetry in the quantum regime of optomechanics using its trilinear radiation pressure interaction is yet to be. We study the connections between local quantum coherence lqc based on wigneryanase skew information and quantum phase transitions qpts. By pairing optical or microwave cavities with mechanical resonators to form a cavity opto mechanical system, one acquires a means to achieve quantum control over mechanical motion or, conversely, mechanical control over optical or microwave fields. As any submicron mechanical resonator, our system demonstrates nonlinear dynamical effects. Quantum measurement with atomic cavity optomechanics. The noncommutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase gates and for precision measurements. Mechanical motion couples to many di erent systems light, atoms, superconducting qubits, microwave resonators, spins, etc. Quantum coherence in ultrastrong optomechanics dan hu,1 shangyu huang, 2jieqiao liao,3 lin tian,1, and hsisheng goan,4 1school of natural sciences, university of california, merced, california 95343, usa 2department of physics and center for theoretical sciences, national taiwan university, taipei 10617, taiwan, republic of china. Such nonlinear effects are expected to play a role in the quantum dynamics of the membrane as well. We analyze the phase conjugate coupling of a pair of optomechanical oscillator modes driven by the timedependent beatnote due to. The phase shift corresponding to the change in the optomechanical cavity length is measured at the interferometer output to estimate the angular velocity of the absolute rotation. Quantum optomechanics radiation pressure hamiltonian is nonlinear for sufficiently strong coupling per single photon g 0 the dynamics will be nongaussian. The authors move on to hybrid optomechanical systems in which the canonical quantum optomechanical system is coupled to another quantum object.
Theory of quantum optomechanics with unconventional nonlinear. In cavity optomechanics significant experimental progress has been made towards quantum state control over mechanical resonators 11, which includes classical phase space monitoring 25, 26, laser cooling close to the ground state 27, 28, and low noise continuous measurement of mechanically induced phase fluctuations 29 31. Limit cycles in the quantum regime niels lorch,1,2 jiang qian,3 aashish clerk,4 florian marquardt,5,6 and klemens hammerer1,2 1institut fur gravitationsphysik, leibniz universitat hannover. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
In particular, the first generation of largescale laser interferometric gravitational wave detectors have passed through their life cycle, meanwhile reaching the sensitivity level close to zeropoint oscillations amplitude of their kilogramscale probe masses and bounded by quantum phase. The onetoone correspondence between operators and phase space functions can be established by a wignerweyl transformation. Osa quantum phase gate for optical qubits with cavity. Dec 22, 2015 it then focuses on the linearized regime of quantum optomechanics before exploring scenarios where the simple linearized picture of quantum optomechanics no longer holds. Recently, optomechanical systems have become a focus for a broad range of research activities 20, 21 and several interesting phenomena like phase conjugation, squeezing, superradiance, laser cooling 3638, optomechanically induced transparency 3943, etc, have been predicted in optomechanics. Quantum optomechanics combines the two perspectives. Absolute rotation detection by coriolis force measurement. A short walk through quantum optomechanics meystre 20. The canonical momenta conjugate to qk and q, pk and p respectively, are obtained. Such a nonlinear enhancement can make the oscillator display chaotic behavior. Introduction to optical phase conjugation opc optical phase conjugation opc 1 is a new laserbased technique developed since 1970s. Cavity optomechanics studies the coupling between a mechanical oscillator and the electromagnetic field in a cavity. We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes.
The photon reflected from phase conjugatingmirror out has opposite directions of linear and angular momenta with respect to incident photon in. Quantum optomechanics quantum technology group at queens. Quantum optomechanics with silicon nanostructures caltech thesis. Qteq has given a great contribution to both the experimental and theoretical efforts in this field. The main motivation for using optics and photonics for information security is that optical waveforms possess many complex degrees of freedom such as amplitude, phase, polarization, large bandwidth, nonlinear transformations, quantum properties of photons, and multiplexing that can be combined in many ways to make information encryption more. A wide range of quantum optomechanical phe nomena can be. An analytic expression for the minimum detectable rotation rate corresponding to the standard quantum limit of measurable coriolis force in the interferometer is derived. Wright, han pu, and pierre meystre, a fundamental limit for integrated atom optics with boseeinstein condensates, phys. At the quantum level, optomechanics can be traced at least as far back as casimir 5. Origin of charge, fine structure constant and inertia.
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