We study the fundamental bounds on precision measurements of parameters contained in a time-depen... more 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.
We study the self gravitation of a quantum system and how it affects the quantum coherence presen... more We study the self gravitation of a quantum system and how it affects the quantum coherence present in its state. The system is initially prepared in a spatial superposition of two different positions of a field excitation, and we employ semiclassical gravity to find its time evolution. Self gravitation affects the coherence initially present in the state of large and heavy systems, whereas light or massless particles are unaffected. The transition between the two scenarios is determined by the ratio of the characteristic size of the system and its Compton length. Furthermore, the phase of the coherence determines the increase or decrease of the probability of locating the system in each of the initial positions. All effects increase linearly with the mass of the particle and time, while they vanish for vanishing coherence in the initial state, for large distances in the spatial superposition, and for massless particles. We believe that our results can explain simultaneously two impo...
We investigate the quantum thermodynamical properties of localised relativistic quantum fields, a... more 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 imp...
We study the time evolution of an ideal system composed of two harmonic oscillators coupled throu... more 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 the dynamics analytically by employing Lie algebraic tools that allow to decouple the time-evolution operator induced by quadratic Hamiltonians. In particular, we use this result to completely chracterize the dynamics of the two oscillators interacting in the ultrastrong coupling regime. 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 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.
We study the full time evolution of one- and two-mode bosonic quantum systems that interact throu... more 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.
Understanding if motion or gravity affects entanglement is fundamental to the possible integratio... more Understanding if motion or gravity affects entanglement is fundamental to the possible integration of quantum theory with relativity and could be relevant in the implementation of new quantum information technologies such as quantum cryptography and teleportation which are currently under investigation in space-based scenarios [1]. In this talk we show employing a quantum optical setting that non-uniform accelerated motion can generate or degrade entanglement and that especial trajectories can be tailored to produced highly entangled twomode squeezed states. We learned from the equivalence principle that there is a correspondence between uniform acceleration and an uniform gravitational field therefore, our results suggest that gravitational effects could produce entanglement. Finding suitable ways to store and process information in a quantum and relativistic setting is a main goal in the field of relativistic quantum information. Recently, uniformly accelerated cavities [2ā 4] hav...
Open system dynamics plays a crucial role in optomechanical systems. Quantum Langevin equations h... more Open system dynamics plays a crucial role in optomechanical systems. Quantum Langevin equations have enabled excellent progress in the field for key parameter regimes, however, a master equation approach valid for all sideband resolutions has thus far proven more elusive. To address this outstanding question, we introduce a new method that combines a Lie-algebra solution of the unitary dynamics with a vectorization of the Lindblad equation. We demonstrate the applicability of our method by computing the fidelity for generating lossy intra-cavity optical cat-states.
We use quantum field theory in curved spacetime to show that gravitational redshift induces a uni... more We use quantum field theory in curved spacetime to show that gravitational redshift induces a unitary transformation on the quantum state of propagating photons. This occurs for realistic photons characterized by a finite bandwidth, while ideal photons with sharp frequencies do not transform unitarily. We find that the transformation is a mode-mixing operation, and we devise a protocol that exploits gravity to induce a Hong-Ou-Mandel-like interference effect on the state of two photons. Testing the results of this work can provide a demonstration of quantum field theory in curved spacetime.
We propose an approach to factorize the time-evolution operator of a quantum system through a (fi... more 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.
We study the non-Gaussian character of quantum optomechanical systems evolving under the fully no... more 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 lightāmatter 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-Gassuianity of the state by driving the lightāmatter 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.
arXiv: General Relativity and Quantum Cosmology, 2016
We propose the idea that not all energy is a source of gravity. We discuss the role of energy in ... more We propose the idea that not all energy is a source of gravity. We discuss the role of energy in the theory of gravitation and provide a formulation of gravity which takes into account the quantum nature of the source. We show that gravity depends dramatically on the entanglement present between the constituents of the Universe. Applications of the theory and open questions are also discussed.
We study the fundamental bounds on precision measurements of parameters contained in a time-depen... more 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.
We study the self gravitation of a quantum system and how it affects the quantum coherence presen... more We study the self gravitation of a quantum system and how it affects the quantum coherence present in its state. The system is initially prepared in a spatial superposition of two different positions of a field excitation, and we employ semiclassical gravity to find its time evolution. Self gravitation affects the coherence initially present in the state of large and heavy systems, whereas light or massless particles are unaffected. The transition between the two scenarios is determined by the ratio of the characteristic size of the system and its Compton length. Furthermore, the phase of the coherence determines the increase or decrease of the probability of locating the system in each of the initial positions. All effects increase linearly with the mass of the particle and time, while they vanish for vanishing coherence in the initial state, for large distances in the spatial superposition, and for massless particles. We believe that our results can explain simultaneously two impo...
We investigate the quantum thermodynamical properties of localised relativistic quantum fields, a... more 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 imp...
We study the time evolution of an ideal system composed of two harmonic oscillators coupled throu... more 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 the dynamics analytically by employing Lie algebraic tools that allow to decouple the time-evolution operator induced by quadratic Hamiltonians. In particular, we use this result to completely chracterize the dynamics of the two oscillators interacting in the ultrastrong coupling regime. 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 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.
We study the full time evolution of one- and two-mode bosonic quantum systems that interact throu... more 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.
Understanding if motion or gravity affects entanglement is fundamental to the possible integratio... more Understanding if motion or gravity affects entanglement is fundamental to the possible integration of quantum theory with relativity and could be relevant in the implementation of new quantum information technologies such as quantum cryptography and teleportation which are currently under investigation in space-based scenarios [1]. In this talk we show employing a quantum optical setting that non-uniform accelerated motion can generate or degrade entanglement and that especial trajectories can be tailored to produced highly entangled twomode squeezed states. We learned from the equivalence principle that there is a correspondence between uniform acceleration and an uniform gravitational field therefore, our results suggest that gravitational effects could produce entanglement. Finding suitable ways to store and process information in a quantum and relativistic setting is a main goal in the field of relativistic quantum information. Recently, uniformly accelerated cavities [2ā 4] hav...
Open system dynamics plays a crucial role in optomechanical systems. Quantum Langevin equations h... more Open system dynamics plays a crucial role in optomechanical systems. Quantum Langevin equations have enabled excellent progress in the field for key parameter regimes, however, a master equation approach valid for all sideband resolutions has thus far proven more elusive. To address this outstanding question, we introduce a new method that combines a Lie-algebra solution of the unitary dynamics with a vectorization of the Lindblad equation. We demonstrate the applicability of our method by computing the fidelity for generating lossy intra-cavity optical cat-states.
We use quantum field theory in curved spacetime to show that gravitational redshift induces a uni... more We use quantum field theory in curved spacetime to show that gravitational redshift induces a unitary transformation on the quantum state of propagating photons. This occurs for realistic photons characterized by a finite bandwidth, while ideal photons with sharp frequencies do not transform unitarily. We find that the transformation is a mode-mixing operation, and we devise a protocol that exploits gravity to induce a Hong-Ou-Mandel-like interference effect on the state of two photons. Testing the results of this work can provide a demonstration of quantum field theory in curved spacetime.
We propose an approach to factorize the time-evolution operator of a quantum system through a (fi... more 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.
We study the non-Gaussian character of quantum optomechanical systems evolving under the fully no... more 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 lightāmatter 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-Gassuianity of the state by driving the lightāmatter 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.
arXiv: General Relativity and Quantum Cosmology, 2016
We propose the idea that not all energy is a source of gravity. We discuss the role of energy in ... more We propose the idea that not all energy is a source of gravity. We discuss the role of energy in the theory of gravitation and provide a formulation of gravity which takes into account the quantum nature of the source. We show that gravity depends dramatically on the entanglement present between the constituents of the Universe. Applications of the theory and open questions are also discussed.
We propose the idea that not all energy is a source of gravity. We discuss the role of energy in ... more We propose the idea that not all energy is a source of gravity. We discuss the role of energy in the theory of gravitation and provide a formulation of gravity which takes into account the quantum nature of the source. We show that gravity depends dramatically on the entanglement present between the constituents of the Universe. Applications of the theory and open questions are also discussed. Does all energy have a weight? A century has passed since the original proposal that energy is the source of gravity. The gravitational nature of energy is now considered a pillar of physics. A change in this view would bring about dramatic consequences to our understanding of the laws of Nature. In this work we propose the idea that not all energy gravitates. This idea stems from considering the role and nature of energy in quantum field theory [1] and semiclassical gravity [2, 3], and by taking into account recent advances in the field of quantum thermodynamics [4]. On the one hand, quantum field theory in curved spacetime and semiclassical gravity cannot account for the quantum nature of gravity, nor can they account for the effects induced by the quantum nature of fields on the gravitational field itself, a phenomenon known as backreaction [3]. On the other, quantum thermodynamics extends the concepts of work, energy and entropy to the quantum realm, far from the thermodynamical limit where statistical fluctuations around the mean become significant [4]. Furthermore , another important difference arises between the two main theories or Nature available, i.e., quantum mechanics and general relativity. Gravity is an intrinsically local theory, while quantum mechanics, on the other hand, is a theory with nonlocal features, i.e., entanglement. A prospective theory of gravitating quantum matter must be able to reconcile these two seemingly incompatible features. We propose a novel formulation of the field equations of gravity that introduces genuine quantum features as a contribution to the source of the dynamics of spacetime. We discuss the main features of the theory and compare preliminary predictions with known results from quantum field theory in curved spacetime [2]. We find that the contribution to gravity of excited fields, i.e., associated with the presence of matter and energy, dramatically depends on their quantum state. For example, quantum matter in a thermal state does contain exci-tations (particles) but might not contribute to the gravitational field at all. In this sense, gravity depends dramatically on the interplay between the purity of the state of the Universe and the purity of the reduced states of its constituents.
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Papers by David E Bruschi