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Estudi teòric i numèric d'un resonador mecànic d'alta qualitat al règim quàntic

Floriach I De Torres, Pol

Published Jul 8, 2024• 0 citations
OpenAlex

Abstract

Continuously measuring the position of a mechanical resonator affects its motion given the right conditions as a result of quantum mechanics. We revisit the quantum trajectories approach for describing the dynamics of such system without introducing a rotating wave approximation for the measurement and obtain its governing equations, assuming an initial Gaussian state. We apply them to assess if we can induce mechanical squeezing on the position of an optomechanical membrane-in-the middle setup through continuous measurement. We further extend them to a multiple-mode case to include the effects of the resonator?s residual modes and, finally, we study and numerically test a feedback cooling method to damp the residual modes and the resonant one simultaneously through means of filtering the measured position.

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•Jan 1, 2018•0 citations
Continuously measuring the position of a mechanical resonator affects its motion given the right conditions as a result of quantum mechanics. We revisit the quantum trajectories approach for describing the dynamics of such system without introducing a rotating wave approximation for the measurement and obtain its governing equations, assuming an initial Gaussian state. We apply them to assess if we can induce mechanical squeezing on the position of an optomechanical membrane-in-the middle setup through continuous measurement. We further extend them to a multiple-mode case to include the effects of the resonator?s residual modes and, finally, we study and numerically test a feedback cooling method to damp the residual modes and the resonant one simultaneously through means of filtering the measured position.
We revisit the stochastic master equation approach to feedback cooling of a quantum mechanical oscillator undergoing position measurement. By introducing a rotating wave approximation for the measurement and bath coupling, we can provide a more intuitive analysis of the achievable cooling in various regimes of measurement sensitivity and temperature. We also discuss explicitly the effect of backaction noise on the characteristics of the optimal feedback. The resulting rotating wave master equation has found application in our recent work on squeezing the oscillator motion using parametric driving and may have wider interest.
nThis thesis comprises of investigations relating to the creation, manipulation, and detection of quantum states in specific configurations of optomechanical and circuit QED systems. Both the unconditional and conditional master equation formalisms are employed toward this end. In the optomechanical context, the lmembrane-in-the-middler system is investigated with regard to its various experimentally demonstrated parametric couplings between optical fields and membrane displacement. Via these couplings, the optical fields are functionalized as probes and controls of the quantum state of a mechanical membrane vibrational mode. In one case, continuous measurement of the optical field is shown to both induce and detect quantum jumps of mechanical energy; the conditions under which this occurs are established and verified in numerical simulations. In a separate case, a scheme is developed that employs simultaneous continuous measurement of two optical fields with distinct parametric couplings to the mem- brane. In this case, it is shown that in situ monitoring and control of the quantum noise profile of a mechanical mode becomes possible. Specifically, the variance of the mechanical energy dis- tribution is numerically shown to monotonically decay with increasing measurement strength of one of the optical fields. In the circuit QED setting, a many-body system is proposed compris- ing of microwave coplanar waveguide resonators arranged in a one-dimensional lattice. Each of the resonators contains a tuneable Kerr nonlinearity that provides an attractive interaction energy for the microwave quanta in the lattice, and each of the resonators is tuneably coupled to its nearest neighbours in the lattice. A scheme is developed under which the tuneability of the parameters is used to effect quantum phase transitions such that initially local microwave resonator quantum states become non-locally superposed across the whole system, thereby providing a feasible route toward deterministically entangling complex microwave resonator states across forty or more resonators. Numerical simulations of the scheme are performed to demonstrate its effectiveness under experimentally accessible parameters.
We study the position estimation of a mechanical oscillator undergoing both detuned parametric amplification and continuous quantum measurement. This model, which can be utilised to produce squeezed states, is applied to a general optoelectromechanical system. Using a stochastic master equation formalism, we derive general formulae for the reduction in position uncertainty of one quadrature of motion. The filter for extracting the optimal position estimate from the measurement record is derived. We also find that since this scheme does not work far into the back-action dominated regime, implementing resolved-sideband cooling improves the squeezing only marginally.
A mechanical system can be optimally controlled through continuous measurements of its position followed by feedback. We revisit the complete formalism for predicting the performance of such a system without invoking the standard rotating-wave approximation and the adiabatic approximation. Using this formalism, we deduce both the conditional and unconditional states of a mechanical oscillator using the optimal control and feedback that leads to mechanical cooling and mechanical squeezing. We find large discrepancies between the exact solutions and the approximate solutions, stressing the importance of using the complete model. We also highlight the importance of distinguishing between the conditional and unconditional states by demonstrating that these two cannot coincide in a typical control scheme, even with infinite feedback strength.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.
Microscopic systems exhibit many intriguing quantum mechanical phenomena which cannot be explained by classical physics. Quantum mechanics has succesfully explained the behaviour of subatomic particles, atoms, and electromagnetic waves where entanglement, wave-particle duality and superposition of particles has been observed. In macroscopic scales, quantum mechanics explains the microscopic origin of electronic properties of solids, and quantum coherence effects are routinely observed in superfluids and superconductors. However, most macroscopic objects behave according to the laws of classical physics due to decoherence effects caused by interaction with the environment. Mechanical systems are ideal for studying quantum behavior of macroscopic objects as they can be measured with high accuracy, and their interaction with the environment can be controlled. Cavity optomechanics studies the interaction between light and mechanical objects through radiation pressure force. Recent developments in the field have made it possible to study quantum behaviour in macroscopic mechanical objects. For example, mechanical oscillators coupled to either microwave or optical light have been cooled to their quantum ground state. This thesis studies a cavity optomechanical system in which micromechanical aluminium membrane resonator is coupled to a superconducting microwave circuit resonator. This work focuses on the phenomena relating to the Heisenberg's uncertainty principle which sets a fundamental limit to the precision in which certain pairs of properties of a system can be measured. Due to uncertainty principle, even if a harmonic oscillator is cooled to the ground state, it still has random motion called the zero-point motion. This sets a fundamental limit on how accurately one can measure the motion of the resonator. In a squeezed quantum state, fluctuations of a quantity can be reduced below this quantum limit, at the cost of increased fluctuations in the pair variable. In this work, motion of a nearly macroscopic object is measured in a squeezed state. Due to uncertainty principle, a measurement amplifying an oscillatory signal always adds noise. However, when information in one part of the signal is lost, one can amplify and measure the other part perfectly. This kind of nearly noiseless phase-sensitive measurement, and squeezing of microwave fields is demonstrated in this work. An optomechanical device that simultaneously performs high-gain amplification and frequency conversion is created. Collective dynamics of a multimode optomechanical system is studied. When measuring the oscillator position continuously, the system is perturbed by the measuring. This can be avoided in quantum back-action evading measurement, which is demonstrated for collective motion of two mechanical resonators. Finally, an entanglement of centre-of-mass motion of two nearly macroscopic objects is created and stabilised.