H. Müller-Ebhardt

An All-Optical Trap for a Gram-Scale Mirror

We report on a stable optical trap suitable for a macroscopic mirror, wherein the dynamics of the mirror are fully dominated by radiation pressure. The technique employs two frequency-offset laser fields to simultaneously create a stiff optical restoring force and a viscous optical damping force. We show how these forces may be used to optically trap a free mass without introducing thermal noise, and we demonstrate the technique experimentally with a 1 g mirror. The observed optical spring has an inferred Youngs modulus of 1.2 TPa, 20% stiffer than diamond. The trap is intrinsically cold and reaches an effective temperature of 0.8 K, limited by technical noise in our apparatus.

Entanglement of macroscopic test masses and the Standard Quantum Limit in laser interferometry

We show that the generation of entanglement of two heavily macroscopic mirrors is feasible with state of the art techniques of high-precision laser interferometry. The basis of such a demonstration would be a Michelson interferometer with suspended mirrors and simultaneous homodyne detections at both interferometer output ports. We present the connection between the generation of entanglement and the standard quantum limit (SQL) for a free mass. The SQL is a well-known reference limit in operating interferometers for gravitational-wave detection and provides a measure of when macroscopic entanglement can be observed in the presence of realistic decoherence processes.

Preparing a mechanical oscillator in non-Gaussian quantum states

We propose a protocol for coherently transferring non-Gaussian quantum states from an optical field to a mechanical oscillator. We demonstrate its experimental feasibility in future gravitational-wave detectors and tabletop optomechanical devices. This work not only outlines a feasible way to investigate nonclassicality in macroscopic optomechanical systems, but also presents a new and elegant approach for solving non-Markovian open quantum dynamics in general linear systems.

Double optical spring enhancement for gravitational wave detectors

Currently planned second-generation gravitational-wave laser interferometers such as Advanced LIGO exploit the extensively investigated signal-recycling technique. Candidate Advanced LIGO configurations are usually designed to have two resonances within the detection band, around which the sensitivity is enhanced: a stable optical resonance and an unstable optomechanical resonance—which is upshifted from the pendulum frequency due to the so-called optical-spring effect. As an alternative to a feedback control system, we propose an all-optical stabilization scheme, in which a second optical spring is employed, and the test mass is trapped by a stable ponderomotive potential well induced by two carrier light fields whose detunings have opposite signs. The double optical spring also brings additional flexibility in reshaping the noise spectral density and optimizing toward specific gravitational-wave sources. The presented scheme can be extended easily to a multi-optical-spring system that allows further optimization.

Local readout enhancement for detuned signal-recycling interferometers

High power detuned signal-recycling interferometers currently planned for second-generation interferometric gravitational-wave detectors (for example Advanced LIGO) are characterized by two resonances in the detection band, an optical resonance and an optomechanical resonance which is upshifted from the suspension pendulum frequency due to the so-called optical-spring effect. The detectors sensitivity is enhanced around these two resonances. However, at frequencies below the optomechanical resonance frequency, the sensitivity of such interferometers is significantly lower than non-optical-spring configurations with comparable circulating power; such a drawback can also compromise high-frequency sensitivity, when an optimization is performed on the overall sensitivity of the interferometer to a class of sources. In this paper, we clarify the reason for such a low sensitivity, and propose a way to fix this problem. Motivated by the optical-bar scheme of Braginsky, Gorodetsky, and Khalili, we propose to add a local readout scheme which measures the motion of the arm-cavity front mirror, which at low frequencies moves together with the arm-cavity end mirror, under the influence of gravitational waves. This scheme improves the low-frequency quantum-noise-limited sensitivity of optical-spring interferometers significantly and can be considered as an incorporation of the optical-bar scheme into currently planned second-generation interferometers. On the other hand it can be regarded as an extension of the optical-bar scheme. Taking compact binary inspiral signals as an example, we illustrate how this scheme can be used to improve the sensitivity of the planned Advanced LIGO interferometer, in various scenarios, using a realistic classical-noise budget. We also discuss how this scheme can be implemented in Advanced LIGO with relative ease.

Quantum state preparation and macroscopic entanglement in gravitational-wave detectors

Long-baseline laser-interferometer gravitational-wave GW detectors are operating at a factor of 10 in amplitude above the standard quantum limit SQL within a broad frequency band in the sense that f f. Such a low-noise budget has already allowed the creation of a controlled 2.7 kg macroscopic oscillator with an effective eigenfrequency of 150 Hz and an occupation number of 200. This result, along with the prospect for further improvements, heralds the possibility of experimentally probing macroscopic quantum mechanics MQM—quantum mechanical behavior of objects in the realm of everyday experience—using GW detectors. In this paper, we provide the mathematical foundation for the first step of a MQM experiment: the preparation of a macroscopic test mass into a nearly minimum-Heisenberg-limited Gaussian quantum state, which is possible if the interferometer’s classical noise beats the SQL in a broad frequency band. Our formalism, based on Wiener filtering, allows a straightforward conversion from the noise budget of a laser interferometer, in terms of noise spectra, into the strategy for quantum-state preparation and the quality of the prepared state. Using this formalism, we consider how Gaussian entanglement can be built among two macroscopic test masses and the performance of the planned Advanced LIGO interferometers in quantum-state preparation.

Probing macroscopic quantum states with a sub-Heisenberg accuracy

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 Diosi [Phys. Lett. A120, 377 (1987)] and Penrose [Gen. Rel. Grav. 28, 581 (1996)].

QND measurements for future gravitational-wave detectors

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit (SQL), a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the SQL significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.

Achieving ground state and enhancing optomechanical entanglement by recovering information

For cavity-assisted optomechanical cooling experiments, in order to achieve the quantum ground state of the mechanical oscillator, the cavity bandwidth needs to be smaller than the mechanical frequency. In the literature, this is the so-called resolved-sideband or good-cavity limit, and this is based on an understanding of optomechanical dynamics. We provide a different but physically equivalent explanation of such a limit: that is, information loss due to finite cavity bandwidth. With an optimal feedback control to recover the information in the cavity output, we can surpass the resolved-sideband limit and achieve the quantum ground state. In addition, recovering this information can also significantly enhance the entanglement between the cavity mode and the mechanical oscillator. Especially when the environmental temperature is high, such optomechanical entanglement will either exist or vanish critically depending on whether information is recovered or not. This provides a vivid example of a quantum eraser in the optomechanical system.

Toward the Quantum Ground State of a Gram-Scale Object

We describe an experiment in which coupling between intense optical fields and mirror oscillators is used for generating squeezed states of light, and also for optically cooling a gram-scale mirror oscillator.