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arXiv:2202.00750 · Physica Scripta

Amplification of mechanical quadratures using weak values

Sergio Carrasco, Miguel Orszag

Published May 31, 2022• 1 citation
arXivHTMLPDF

Abstract

Abstract An interferometric arrangement is proposed in which the technique of weak value amplification is implemented in order to enlarge the effect of a single photon on the quadratures of a movable mirror of an optical cavity. The photon interacts weakly with the mirror via radiation pressure and is postselected in the dark port of the interferometer. The real and imaginary parts of weak values of angular momentum type photonic operators produce an amplification of the mirror quadratures, which is large as compared to the scenario in which all photons are taken into consideration, i.e. when no postselection is performed. The effect is studied both for a mirror initialized in a thermal and coherent states. For a thermal state, the weak value amplification effect is boosted with the number of particles of the mirror, which occurs due to the imaginary part of the weak values.

DOI
10.1088/1402-4896/ac74eb

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Abstract An interferometric arrangement is proposed in which the technique of weak value amplification is implemented in order to enlarge the effect of a single photon on the quadratures of a movable mirror of an optical cavity. The photon interacts weakly with the mirror via radiation pressure and is postselected in the dark port of the interferometer. The real and imaginary parts of weak values of angular momentum type photonic operators produce an amplification of the mirror quadratures, which is large as compared to the scenario in which all photons are taken into consideration, i.e. when no postselection is performed. The effect is studied both for a mirror initialized in a thermal and coherent states. For a thermal state, the weak value amplification effect is boosted with the number of particles of the mirror, which occurs due to the imaginary part of the weak values.
An experimental proposal is presented in which dark port postselection together with weak measurements are used to enlarge the radiation pressure effect of a single photon on a mechanical oscillator placed in the middle of a Fabry-P\'erot cavity and initialized in the ground state. By preparing and postselecting the photon (the system) in two quasiorthogonal states, the weak value of the radiation force operator can lie outside the eigenvalue spectrum, producing a large shift on the wave function of the mechanical oscillator (the measuring device) in the position representation. Consequently, the effect of a single photon on the average position of the oscillator can be amplified as compared to the effect caused by a photon without postselection, i.e., only preselected. The strong measurement scenario is also analyzed. In this case, a higher amplification effect is achieved and the mean position of the oscillator can reach the level of the zero-point fluctuations, but the postselection probabilities are smaller. Finally, the situation in which the oscillator starts in a thermal equilibrium state is studied. In this case, the amplification of the average position remains the same, i.e., proportional to the weak value, but the signal-to-noise ratio is reduced by a factor that depends on the average number of thermal phonons.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
A measurement of an observable A performed on a quantum system that is initially prepared in a state ρi, followed by a probabilistic procedure that leaves the system in a final state ρf, a process often referred as state postselection (or filtering process), can yield, on average, anomalous measurement results, i.e., values that may exceed the eigenvalue range of the observable being measured or be complex numbers. There is, therefore, an amplification effect of the average measurement result, i.e., the effect of the system on the measurement device is increased. When the coupling between the system and the measurement device satisfies some weakness conditions, the amplification effect occurs due to the weak value of the operator A. In this article, the amplification effect due to the postselection process is reviewed, and theoretical proposals and experiments published in the recent literature on the field are commented on. The emphasis is made on interactions occurring in optical nonlinear media and opto-mechanical and spin-mechanical systems, in which the amplification of number operators takes place.
In this article we present an experimental proposal for quantum enhanced estimation of optomechanical parameters. The precision of the estimation is improved by using the technique of weak value amplification, which can enlarge the radiation pressure effect of a single-photon on a nano/micro mechanical oscillator. This task is accomplished by using two interferometric setups. Single-photon pulses are sent through one interferometer, producing a maximally path entangled state which drives the cavity optomechanical system. The photons are then postselected in one of the detectors in the output. A second interferometer, whose operation is triggered by every successful postselection, performs an optical measurement of the phase shift generated by the optomechanical system on a classical beam, which encodes the information of the optomechanical parameters. In the presence of fully time-correlated noise, we show that the Fisher information is improved as compared to a standard measurement that employs no postselection.
In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak-value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak-value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise, the weak-value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.