Phase space structure of generalized Gaussian cat states

Nicacio, F.; Maia, Raphael N. P.; Toscano, Fabricio; Vallejos, Raúl O.

doi:10.1016/j.physleta.2010.08.076

Cited by 22 publications

(33 citation statements)

References 55 publications

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“…We can however not apply directly formula (53) since S is not a Hilbert-Schmidt operator. Let us proceed as follows: in view of formula (39) in Proposition 12. The twisted Weyl symbol c σ of C is given by the absolutely convergent integral…”

Section: A General Resultsmentioning

confidence: 99%

“…However, any quantum state can be expanded as a superposition of (Gaussian) coherent states, thus this method can be applied to the propagation of any initial state [9,32]. An example for the propagation of states under a non-linear (and classically chaotic) Hamiltonian dynamics is given in [39].…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

“…Our central result is placed in theorem 21 which now will be slightly generalized to a larger class of Hamiltonian dynamics, besides the quadratic term we will include affine transformations related to phase space displacements. Despite its simplicity, the new form of the Hamiltonian is widely used in the literature as an approximation for any Hamiltonian dynamical system, see for instance [9,32,39].…”

Section: The Inhomogeneous Casementioning

confidence: 99%

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Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states

Gosson

Nicacio

2018

Journal of Mathematical Physics

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We address in this paper the notion of relative phase shift for mixed quantum systems. We study the Pancharatnam-Sjöqvist phase shift ϕ(t) = Arg Tr( U t ρ) for metaplectic isotopies acting on Gaussian mixed states. We complete and generalize previous results obtained by one of us while giving rigorous proofs. This gives us the opportunity to review and complement the theory of the Conley-Zehnder index which plays an essential role in the determination of phase shifts.

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Section: A General Resultsmentioning

confidence: 99%

Section: Discussion and Perspectivesmentioning

confidence: 99%

Section: The Inhomogeneous Casementioning

confidence: 99%

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Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states

Gosson

Nicacio

2018

Journal of Mathematical Physics

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“…(See the appendix C or [36][37][38][39] for the derivation.) From here, the application of the map in an infinitesimal time δt can be identified as:…”

Section: Fdt For Lindbladian Master Equationsmentioning

confidence: 99%

Linear response theory for quantum Gaussian processes

2019

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Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

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“…Being quadratic the master equation Eq. (3) evolves Gaussian states to Gaussian states [62][63][64]. Eq.…”

Section: Introductionmentioning

confidence: 99%

Quantum enhanced estimation of diffusion

et al. 2019

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Momentum diffusion is a possible mechanism for driving macroscopic quantum systems towards classical behaviour. Experimental tests of this hypothesis rely on a precise estimation of the strength of this diffusion. We show that quantum-mechanical squeezing offers significant improvements, including when measuring position. For instance, with 10 dB of mechanical squeezing, experiments would require a tenth of proposed free-fall times. Momentum measurement is better by an additional factor of three, while another quadrature is close to optimal. These have particular implications for the space-based MAQRO proposal-where it could rule out the spontaneous collapse theory due to Ghirardi, Rimini, and Weber-as well as terrestrial optomechanical sensing.

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Phase space structure of generalized Gaussian cat states

Cited by 22 publications

References 55 publications

Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states

Relative phase shifts for metaplectic isotopies acting on mixed Gaussian states

Linear response theory for quantum Gaussian processes

Quantum enhanced estimation of diffusion

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