A Macroscopic Mechanical Oscillator at the Quantum Limit Level: a Practical Scheme.

Vladimir B. Braginskii, V. S. Nazarenko

Haixing Miao, S. L. Danilishin, H. Müller‐Ebhardt +3 more

Significant achievements in high-sensitivity measurements will soon allow us to probe quantum behaviors of macroscopic mechanical oscillators. In a recent work [Phys. Rev. A 80, 043802 (2009)], we formulated a general framework for treating preparation of Gaussian quantum states of macroscopic oscillators through linear position measurements. To outline a complete procedure for testing macroscopic quantum mechanics, here we consider a subsequent verification stage which probes the prepared macroscopic quantum state and verifies the quantum dynamics. By adopting an optimal time-dependent homodyne detection in which the phase of the local oscillator varies in time, the conditional quantum state can be characterized below the Heisenberg limit, thereby achieving a quantum tomography. In the limiting case of no readout loss, such a scheme evades measurement-induced back action, which is identical to the variational-type measurement scheme invented by Vyatchanin et al. [JETP 77, 218 (1993)] but in the context for detecting gravitational waves. To motivate macroscopic quantum mechanics experiments with future gravitational-wave detectors, we mostly focus on the parameter regime where the characteristic measurement frequency is much higher than the oscillator frequency and the classical noises are Markovian, which captures the main feature of a broadband gravitational-wave detector. In addition, we discuss verifications of Einstein-Podolsky-Rosen-type entanglement between macroscopic test masses in future gravitational-wave detectors, which enables us to test one particular version of gravity decoherence conjectured by Di\'osi [Phys. Lett. A120, 377 (1987)] and Penrose [Gen. Rel. Grav. 28, 581 (1996)].

Swati Singh

This thesis concentrates on generating and measuring non-classical states of mechanical oscillators by coupling them to atomic and molecular quantum systems. We start with a discussion of what novel physics can be explored by mechanical systems operating in the quantum regime. We then discuss one technique making it a possibility- cavity optomechanics, particularly optomechanical cooling. We investigate the limits of optomechanical cooling and review how the coupling of mechanical oscillators to external heat baths limits the minimum attainable phonon occupation number. As a possible alternative for circumventing clamping losses, we consider an all-optical approach where the mechanical element (in this case, a Bragg mirror) is suspended via optical forces, and discuss some limitations of this approach. We explore several schemes aimed at the generation of quantum states in mechanical oscillators. We consider specifically two examples: one in which the mechanical oscillator is coupled to polar molecules via dipole-dipole interaction, and another where it is magnetically coupled to a Bose condensate. The first example emphasizes that such an interaction can generate parametric squeezing and entanglement. The second scheme demonstrates that the back action of BEC spin measurements can be used to generate quantum states of motion of a mechanical oscillator. We then discuss possible methods for measuring the entire density matrix of a mechanical oscillator. The first method achieves the tomographic reconstruction of the mechanical Wigner function by coupling it simultaneously to a classical optical oscillator and a qubit. The second approach involves a state transfer scheme between momentum excitations of a bose-condensate in a cavity and a moving mirror of the cavity that is entirely mediated by the light field. We conclude with a discussion of the broader implications of this work, and some future research directions.

Yuri S. Kivshar, Tristram J. Alexander, Sergei K. Turitsyn

Konrad W. Lehnert

Vladimir B. Braginskii, Yurii I. Vorontsov

Perfection of the technique of macroscopic physical experiments has recently been proceeding so intensively that we can now inquire naturally under what conditions in macroscopic experiments will an increase in sensitivity be limited by the quantum-mechanical properties of the test objects. In this article we determine the limiting values of the detectable accelerations (or forces) when free particles or oscillators are used as the test objects. The conditions for attaining the limiting sensitivity are discussed. It is shown possible to increase the sensitivity of a converter of mechanical into electrical oscillations by increasing the relaxation time of the electric resonator. The possibility is discussed of nondestructive recording of the n -quantum state of an oscillator. It is shown with the example of a concrete experimental design that one can determine the value of n (including n = 0) in such a way that the probability of transition to the adjacent levels after the measurement will be small.