Improvement of precision in gravimetry is an important problem in detecting the gravitational waves. In The first demonstration of using quantum optomechanical cavity in gravimetry has recently been reported. This experiment has been done by employing a cooled levitated nano-sphere as a mechanical oscillator in its ground state coupled to a cavity electrodynamics. Following this experiment, in a recent proposal, a quantum optomechanical system has been used for measuring of gravitational acceleration. A generic setup for gravimetry purposes, containing two couples optomechanical cavities, where mirrors play the role of oscillating parts. We study such quantum mechanical system, by investigation the dynamics of entanglement between different parts of two coupled cavity optomechanical cells. For such setup, optimal conditions for predesignated entanglement behavior, based on some important parameters of the system, like photon-photon and photon-phonon couplings, electromagnetic field strength and mechanical mode of moving mirrors are analyzed numerically. We show that there exist two different behaviors for entanglement according to selected values for the system parameters.
Improvement of precision in gravimetry is an important problem in detecting the gravitational waves. In The first demonstration of using quantum optomechanical cavity in gravimetry has recently been reported. This experiment has been done by employing a cooled levitated nano-sphere as a mechanical oscillator in its ground state coupled to a cavity electrodynamics. Following this experiment, in a recent proposal, a quantum optomechanical system has been used for measuring of gravitational acceleration. A generic setup for gravimetry purposes, containing two couples optomechanical cavities, where mirrors play the role of oscillating parts. We study such quantum mechanical system, by investigation the dynamics of entanglement between different parts of two coupled cavity optomechanical cells. For such setup, optimal conditions for predesignated entanglement behavior, based on some important parameters of the system, like photon-photon and photon-phonon couplings, electromagnetic field strength and mechanical mode of moving mirrors are analyzed numerically. We show that there exist two different behaviors for entanglement according to selected values for the system parameters.
The field of cavity optomechanics is based on the coupling of optical cavities to mechanical degrees of freedom. Over the past two decades, it has led to remarkable and surprising discoveries. A cavity optomechanical system enabled the first observation of gravitational waves, a discovery awarded with the 2017 Nobel prize, confirming Einstein's 100-year-old prediction. It was also a cavity optomechanical system that has for the first time enabled ground state cooling of the motion of an object containing ~1012 atoms, and entanglement of mechanical oscillators of similar size. Moreover, cavity optomechanical systems have facilitated significant progress in precision-sensing technologies, with diverse applications such as biosensing, magnetometry, and many more.But this may only be the beginning. The field is still in its early days and experimental capabilities are improving fast. For instance, cavity optomechanical systems have the potential to test predicted signatures of quantum gravity such as modifications to the canonical commutator, short-distance modifications to Newtonian gravity, dark matter and dark energy, and even extra dimensions. In this sense, they form an economical platform with a short experimental turnover time, that can compete in its predictive power with mega-scale, multi-billion-dollar experiments such as the Large Hadron Collider.This thesis is dedicated to utilizing cavity optomechanics to explore the maybe most challenging and unexplored frontier in quantum mechanics: The dynamics of macroscopic quantum systems. Quantum physics, since its discovery in the early 20th century, has revolutionized our understanding of the microworld, but has long been thought to apply exclusively to extremely small objects. However, over the past decades, ever-larger quantum systems have emerged in laboratories around the world. On one hand, these are collective, macroscopic quantum phenomena such as superfluidity, superconductivity, and Bose-Einstein condensation. On the other hand, they are quantum states of relatively massive mechanical objects. While our understanding of the interplay of quantum mechanical and classical systems has greatly improved over the past decades, as described by theories of decoherence and open quantum systems, many basic questions about macroscopic quantum systems still remain unanswered. Quantum fluids such as Bose-Einstein condensates and superfluid helium are inherently hard to understand due to their complex dynamics, and difficult to probe experimentally due to the weakness of their interactions with the environment and their fragile nature. This is especially true in the strongly-interacting regime, which is, for instance, found in superfluid helium.Another long-standing, unanswered set of questions in quantum mechanics is related to the quantum measurement problem. What constitutes a quantum measurement? What happens if we engineer a quantum state that is large enough to be, in principle, part of our everyday world? What if we attempt to create a quantum superposition of a living being? Do the laws of physics even permit either of these scenarios?Cavity optomechanics is a unique and powerful platform to investigate macroscopic quantum systems. The extreme sensitivity of cavity optomechanical sensors in readout of mechanical motion makes them susceptible to minute quantum effects. The strong coupling between single photons and phonons in these systems allows engineering and measurement of quantum states of mechanical systems. Furthermore, most cavity optomechanical experiments are cryo-compatible and small in size, which allows integration with other quantum systems to be analyzed, such as superfluid helium.
We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. The optomechanical system consists of a cavity mode and a mechanical oscillator coupled to it via (non-linear) radiation pressure coupling. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can be further enhanced by injecting squeezed states of the cavity field or by modulating the light–matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nanogram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.
Abstract We explore how to measure the gravitational acceleration by using a dissipative optomechanical cavity. What is quite different from the conventional measurement methods is that we have constructed a nonreciprocal optomechanical coupling. We demonstrate that nonreciprocal coupling has a much greater advantage than reciprocal coupling. When the coherent optomechanical coupling is relatively weak and the driving intensity of single photon is strong, nonreciprocal coupling can improve the measurement precision by a factor of two. When the driving strength of single photon tends to infinity, reciprocal coupling fails to obtain any information about the gravitational acceleration, while nonreciprocal coupling still does. Using a two-photon driving, the measurement uncertainty of the gravitational acceleration will tend to zero as the intensity of two-photon driving approaches the critical point. The critical value of the two-photon driving intensity required for nonreciprocal coupling is finite, but the critical value of the two-photon driving intensity required for reciprocal coupling is infinite. The combination of the amplification of mechanical parameters and the extra force can not improve the measurement precision, but it can enhance the susceptibility. Furthermore, when the single-photon driving field is relatively weak, we analytically calculate the quantum Fisher information. The results show that, under most experimental parameters, nonreciprocal coupling still performs better than reciprocal coupling.
We study the fundamental sensitivity that can be achieved with an ideal optomechanical system in the nonlinear regime for measurements of time-dependent gravitational fields. Using recently developed methods to solve the dynamics of a nonlinear optomechanical system with a time-dependent Hamiltonian, we compute the quantum Fisher information for linear displacements of the mechanical element due to gravity. We demonstrate that the sensitivity can not only be further enhanced by injecting squeezed states of the cavity field, but also by modulating the light--matter coupling of the optomechanical system. We specifically apply our results to the measurement of gravitational fields from small oscillating masses, where we show that, in principle, the gravitational field of an oscillating nano-gram mass can be detected based on experimental parameters that will likely be accessible in the near-term future. Finally, we identify the experimental parameter regime necessary for gravitational wave detection with a quantum optomechanical sensor.
We present a table-top quantum estimation protocol to measure the gravitational acceleration g by using an optomechanical cavity. In particular, we exploit the nonlinear quantum light-matter interaction between an optical field and a massive mirror acting as mechanical oscillator. The gravitational field influences the system dynamics affecting the phase of the cavity field during the interaction. Reading out such a phase carried by the radiation leaking from the cavity, we provide an estimate of the gravitational acceleration through interference measurements. Contrary to previous studies, having adopted a fully quantum description, we are able to propose a quantum analysis proving the ultimate bound to the estimability of the gravitational acceleration and verifying optimality of homodyne detection. Noticeably, thanks to the light-matter decoupling at the measurement time, no initial cooling of the mechanical oscillator is demanded in principle.
The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of 10−6g/Hz. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.