arXiv subjects

David Edward Bruschi

Publications and source records attributed to David Edward Bruschi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Interplay between optomechanics and the dynamical Casimir effect

We develop a model of a quantum field confined within a cavity with a movable wall where the position of the wall is quantized. We obtain a full description of the dynamics of both the quantum field and the confining wall depending on the initial state of the whole system. Both the reaction and back-reaction of the field on the wall, and the wall on the field, can be taken into account, as well as external driving forces on both the cavity and the wall. The model exactly reproduces the resonant cavity mode stimulation due to the periodic motion of the mirror (dynamical Casimir effect), as well as the standard radiation pressure effects on the quantized wall(optomechanics). The model also accounts for the interplay of the two scenarios. Finally, the time evolution of the radiation force shows the interplay between the static and dynamical Casimir effect.

quant-ph↗

arXiv2022

Spacetime effects on wavepackets of coherent light

We investigate the interplay between gravity and the quantum coherence present in the state of a pulse of light propagating in curved spacetime. We first introduce an operational way to distinguish between the overall shift in the pulse wavepacket and its genuine deformation after propagation. We then apply our technique to quantum states of photons that are coherent in the frequency degree of freedom, as well as to states of completely incoherent light. We focus on Gaussian profiles and frequency combs and find that the quantum coherence initially present can enhance the deformation induced by propagation in a curved background. These results further supports the claim that genuine quantum features, such as quantum coherence, can be used to probe the gravitational properties of physical systems. We specialize our techniques to Earth-to-satellite communication setups, where the effects of gravity are weak but can be tested with current satellite technologies.

quant-ph↗

arXiv2022

Observer dependence of photon bunching: The influence of the relativistic redshift on Hong-Ou-Mandel interference

We study the influence of the relativistic redshift on Hong-Ou-Mandel (HOM) interference, and present a genuine quantum test of general relativity. We use Glauber's theory of quantum coherence to predict the coincidence probability of realistic broadband photons in HOM-experiments in a non-relativistic setting. We extend the quantum field theoretical framework previously developed to describe the deformation of the spectral profile of single photons in curved spacetimes to a multi-photon framework, which is exact for inertial observers in a flat spacetime and an approximation when observers are located in a curved spacetime. We find that, in case of frequency entangled photons, a mutual redshift between the sender and the receiver can change the coincidence statistics from photon bunching to photon anti-bunching, and vice versa. This implies that the (anti-) symmetry of the photonic spectral wave function is an observer dependent notion, and that this can be probed via HOM-experiments in a relativistic setting.

gr-qc↗

arXiv2021

Master-equation treatment of nonlinear optomechanical systems with optical loss

Open-system dynamics play a key role in the experimental and theoretical study of cavity optomechanical systems. In many cases, the quantum Langevin equations have enabled excellent models for optical decoherence, yet a master-equation approach to the fully nonlinear optomechanical Hamiltonian has thus far proven more elusive. To address this outstanding question and broaden the mathematical tool set available, we derive a solution to the Lindblad master equation that models optical decoherence for a system evolving with the nonlinear optomechanical Hamiltonian. The method combines a Lie-algebra solution to the unitary dynamics with a vectorization of the Lindblad equation, and we demonstrate its applicability by considering the preparation of optical cat states via the optomechanical nonlinearity in the presence of optical loss. Our results provide a direct way of analytically assessing the impact of optical decoherence on the optomechanical intracavity state.

quant-ph↗

arXiv2021

Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems

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.

quant-ph↗

arXiv2021

Factorizing time evolution into elementary steps

We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques and other factorization procedures, and requires a set of optimization operations that provide the final result. Concretely, the algorithm produces at each step three optimal quantities, namely the optimal duration of the desired unitary operation, the optimal functional dependence of the driving function on the optimal time, and the optimal elementary Hermitian operation that induces the additional unitary operation to be implemented. The resulting sequence of unitary operations that is obtained this way is sequential with time. We compare our proposal with existing approaches, and highlight which key assumptions can be relaxed for practical implementations.

quant-ph↗

arXiv2021

General solution of the time evolution of two interacting harmonic oscillators

We study the time evolution of an ideal system composed of two harmonic oscillators coupled through a quadratic Hamiltonian with arbitrary interaction strength. We solve its dynamics analytically by employing tools from symplectic geometry. In particular, we use this result to completely characterize the dynamics of the two oscillators interacting in the ultrastrong coupling regime with additional single-mode squeezing on both oscillators, as well as higher order terms. Furthermore, we compute quantities of interest, such as the average number of excitations and the correlations that are established between the two subsystems due to the evolution. We find that this model predicts a second order phase transition and we compute the critical exponents and the critical value. We also provide an exact decoupling of the time evolution in terms of simple quantum optical operations, which can be used for practical implementations and studies. Finally, we show how our techniques can be extended to include more oscillators and higher order interactions.

quant-ph↗

arXiv2020

Thermodynamics of relativistic quantum fields confined in cavities

We investigate the quantum thermodynamical properties of localised relativistic quantum fields, and how they can be used as quantum thermal machines. We study the efficiency and power of energy transfer between the classical gravitational degrees of freedom, such as the energy input due to the motion of boundaries or an impinging gravitational wave, and the excitations of a confined quantum field. We find that the efficiency of energy transfer depends dramatically on the input initial state of the system. Furthermore, we investigate the ability of the system to extract energy from a gravitational wave and store it in a battery. This process is inefficient in optical cavities but is significantly enhanced when employing trapped Bose Einstein condensates. We also employ standard fluctuation results to obtain the work probability distribution, which allows us to understand how the efficiency is related to the dissipation of work. Finally, we apply our techniques to a setup where an impinging gravitational wave excites the phononic modes of a Bose Einstein condensate. We find that, in this case, the percentage of energy transferred to the phonons approaches unity after a suitable amount of time. These results give a quantitative insight into the thermodynamic behaviour of relativistic quantum fields confined in cavities.

quant-ph↗

arXiv2020

Enhanced continuous generation of non-Gaussianity through optomechanical modulation

We study the non-Gaussian character of quantum optomechanical systems evolving under the fully nonlinear optomechanical Hamiltonian. By using a measure of non-Gaussianity based on the relative entropy of an initially Gaussian state, we quantify the amount of non-Gaussianity induced by both a constant and time-dependent cubic light-matter coupling and study its general and asymptotic behaviour. We find analytical approximate expressions for the measure of non-Gaussianity and show that initial thermal phonon occupation of the mechanical element does not significantly impact the non-Gaussianity. More importantly, we also show that it is possible to continuously increase the amount of non-Gaussianity of the state by driving the light-matter coupling at the frequency of mechanical resonance, suggesting a viable mechanism for increasing the non-Gaussianity of optomechanical systems even in the presence of noise.

quant-ph↗

arXiv2020

Time-evolution of nonlinear optomechanical systems: Interplay of mechanical squeezing and non-Gaussianity

We solve the time evolution of a nonlinear optomechanical Hamiltonian with arbitrary time-dependent mechanical displacement, mechanical single-mode squeezing and a time-dependent optomechanical coupling up to the solution of two second-order differential equations. The solution is based on identifying a minimal and finite Lie algebra that generates the time-evolution of the system. This reduces the problem to considering a finite set of coupled ordinary differential equations of real functions. To demonstrate the applicability of our method, we compute the degree of non-Gaussianity of the time-evolved state of the system by means of a measure based on the relative entropy of the non-Gaussian state and its closest Gaussian reference state. We find that the addition of a constant mechanical squeezing term to the standard optomechanical Hamiltonian generally decreases the overall non-Gaussian character of the state. For sinusoidally modulated squeezing, the two second-order differential equations mentioned above take the form of the Mathieu equation. We derive perturbative solutions for a small squeezing amplitude at parametric resonance and show that they correspond to the rotating-wave approximation at times larger than the scale set by the mechanical frequency. We find that the non-Gaussianity of the state increases with both time and the squeezing parameter in this specific regime.

quant-ph↗

arXiv2020

Optimal estimation with quantum optomechanical systems in the nonlinear regime

We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a single-mode mechanical squeezing term. By using a recently developed method to solve the dynamics of this system, we derive a general expression for the quantum Fisher information and demonstrate its applicability through three concrete examples: estimation of the strength of a nonlinear light-matter coupling, the strength of a time-modulated mechanical displacement, and a single-mode mechanical squeezing parameter, all of which are modulated at resonance. Our results can be used to compute the sensitivity of a nonlinear optomechanical system to a number of external and internal effects, such as forces acting on the system or modulations of the light--matter coupling.

quant-ph↗

arXiv2019

Wigner phase of photonic helicity states in the spacetime of the Earth

We study relativistic effects on polarised photons that travel in a curved spacetime. As a concrete application, we consider photons in the gravitational field of the Earth, on a closed path that starts at a terrestial laboratory, is reflected at one or more satellites, and finally returns to the laboratory. We find that the photons acquire a non-trivial Wigner phase already when the gravitational field is static, such as the Schwarzschild spacetime, where previous studies have found a trivial Wigner phase for closed photon paths. A gauge-invariant description of this nontrivial Wigner phase remains an open question, to be resolved before the formalism can provide predictions for experiments.

quant-ph↗

arXiv2019

Time evolution of coupled multimode and multiresonator optomechanical systems

We study the time evolution of bosonic systems where multiple driven bosonic modes of light interact with multiple mechanical resonators through arbitrary, time-dependent, optomechanical-like interactions. We find the analytical expression for the full time evolution of the system and compute the expectation value of relevant quantities of interest. Among the most interesting ones, we are able to compute the first-order quantum bipartite coherence between pairs of subsystems, and the analytical expression for the mixedness induced by the nonlinear interaction in the reduced state of the mechanical oscillators. Finally, we also compare our results with a linearised version of the system, and we find a regime where there are qualitative and quantitative differences in the behavior of some measurable quantities. Our results can therefore be used to describe the full time-evolution of the system, to characterise its nonlinear character and explore the validity of the linearisation approach.

quant-ph↗

arXiv2019

Time evolution of two harmonic oscillators with cross-Kerr interactions

We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution operator and obtain the analytical solution for the time evolution of the system. We apply these results to obtain explicit expressions of a few quantities of interest. Our results do not require approximations and therefore allow to study the nature and implications of the full nonlinearity of the system. Potential applications and extensions to optomechanics are also discussed.

quant-ph↗

arXiv2019

Quantum-metrology estimation of spacetime parameters of the Earth outperforming classical precision

We consider quantum communication schemes where quantum optical signals are exchanged between a source on Earth and a satellite. The background curved spacetime affects the quantum state of the propagating photons. We employ quantum-metrology techniques to obtain optimal bounds for the precision of quantum measurements of relevant physical parameters encoded in the final state. We focus on satellites in low Earth orbits and we find that our scheme improves the precision of the measurement of the Schwarzschild radius obtained within previous studies. Therefore, our techniques can provide the theoretical tools for novel developments that can potentially outperform the state-of-the-art obtained through classical means. We also review the impact of the relativistic effects on a simple quantum key distribution protocol within satellite schemes and find that such effects can be greatly damaging if they are not properly accounted for.

quant-ph↗

arXiv2018

Work drives time evolution

We propose the idea that time evolution of quantum systems is driven by work. The formalism presented here falls within the scope of a recently proposed theory of gravitating quantum matter where extractible work, and not energy, is responsible for gravitation. Our main assumption is that extractible work, and not the Hamiltonian, dictates dynamics. We find that expectation values of meaningful quantities, such as the occupation number, deviate from those predicted by standard quantum mechanics. The scope, applications and validity of this proposal are also discussed.

quant-ph↗

arXiv2018

Time evolution of interacting bosons through squeezing Hamiltonians

We study the full time evolution of one- and two-mode bosonic quantum systems that interact through single- and two-mode squeezing Hamiltonians. We establish that the single- and two-mode cases are formally equivalent, leading to the same differential equations encoding the full time evolution. These differential equations can be easily employed in any application. We analytically predict a dramatic transition in the population of the modes when the coupling takes a specific critical value, leading to exponential growth of the excitation population. We discuss the validity, scope and generality of our results.

quant-ph↗

arXiv2018

Space QUEST mission proposal: Experimentally testing decoherence due to gravity

Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009, T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.

quant-ph↗