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.
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.
Long-baseline laser-interferometer gravitational-wave (GW) detectors are operating at a factor of $\ensuremath{\sim}10$ (in amplitude) above the standard quantum limit (SQL) within a broad frequency band (in the sense that $\ensuremath{\Delta}f\ensuremath{\sim}f$). 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 $\ensuremath{\sim}200$. 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.
In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror motion in interferometric gravitational wave detectors was proposed, with the aim of testing quantum theory in the regime of macroscopic objects, and to make available nonclassical probe systems for future tests of modified quantum theories that include (non-relativistic) gravity. The work presented here builds on these earlier results and proposes a specific Michelson interferometer that includes two high-quality laser mirrors of about 0.1 kg mass each. The mirrors are individually suspended as pendula and located close to each other, and cooled to about 4 K. The physical concepts for the generation of the EPR-entangled centre of mass motion of these two mirrors are described. Apart from a test of quantum mechanics in the macroscopic world, the setup is envisioned to test predictions of yet-to-be-elaborated modified quantum theories that include gravitational effects.
Abstract The measurement of minuscule forces and displacements with ever greater precision is inhibited by the Heisenberg uncertainty principle, which imposes a limit to the precision with which the position of an object can be measured continuously, known as the standard quantum limit1–4. When light is used as the probe, the standard quantum limit arises from the balance between the uncertainties of the photon radiation pressure applied to the object and of the photon number in the photoelectric detection. The only way to surpass the standard quantum limit is by introducing correlations between the position/momentum uncertainty of the object and the photon number/phase uncertainty of the light that it reflects5. Here we confirm experimentally the theoretical prediction5 that this type of quantum correlation is naturally produced in the Laser Interferometer Gravitational-wave Observatory (LIGO). We characterize and compare noise spectra taken without squeezing and with squeezed vacuum states injected at varying quadrature angles. After subtracting classical noise, our measurements show that the quantum mechanical uncertainties in the phases of the 200-kilowatt laser beams and in the positions of the 40-kilogram mirrors of the Advanced LIGO detectors yield a joint quantum uncertainty that is a factor of 1.4 (3 decibels) below the standard quantum limit. We anticipate that the use of quantum correlations will improve not only the observation of gravitational waves, but also more broadly future quantum noise-limited measurements.
Laser interferometers are quantum instruments. This chapter presents the quantum theory of laser interferometer gravitational wave detectors. We show the basics for analysing the quantum noise in the detector, and for deriving the associated standard quantum limit (SQL) for the sensitivity. By providing different perspectives on the origin of the SQL, we illustrate the motivations behind different approaches for surpassing the SQL. Introduction The most difficult challenge in building a laser interferometer gravitational wave (GW) detector is isolating the test masses from the rest of the world (e.g. random kicks from residual gas molecules, seismic activities, acoustic noises, thermal fluctuations, etc.) whilst keeping the device locked around the correct point of operation (e.g. pitch and yaw angles of the mirrors, locations of the beam spots, resonance condition of the cavities, and darkport condition for the Michelson). Once all these issues have been solved, we arrive at the issue that we are going to analyse in this chapter: the fundamental noise that arises from quantum fluctuations in the system. A simple estimate (following the steps of Braginsky, 1968) will already lead us into the quantum world – as it will turn out, the superb sensitivity of gravitational wave detectors will be constrained by the standard quantum limit (SQL), which relates to the fundamental heisenberg uncertainty principle . Further improvements of detector sensitivity beyond this require us to manipulate the quantum coherence of light to our advantage. In this chapter, we will introduce how to analyse GW detectors quantum mechanically, and will describe several advanced configurations to surpass the SQL.
The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of quatum fluctuations on the measurement sensitivity, and the quantum mechanics of macroscopic objects: to try to prepare, manipulate and characterize the quantum state of a macroscopic quantum object through quantum measurement. Quantum noise leads to the Standard Quantum Limit (SQL), which provides the magnitude in which we must consider both measurement precision and measurement-induced back-action. The beginning of the chapter will be devoted to this thread of thought. The free-mass SQL actually provides a benchmark for the ‘quantum-ness’ of the system. We will show that a sub-SQL device can be used to prepare nearly pure quantum states and mechanical entanglement, as well as non-Gaussian quantum states that have no classical counterparts.