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arXiv:1604.07237 · Physical Review A

Work distribution in a photonic system

M. A. A. Talarico, P. B. Monteiro, E. C. Mattei, Eduardo I. Duzzioni, P. H. Souto Ribeiro, Lucas C. Céleri

Published Oct 5, 2016• 10 citations
arXivHTMLPDF

Abstract

We present a proposal of a setup to measure the work distribution of a process acting on a quantum system emulated by the transverse degrees of freedom of classical light. Hermite-Gaussian optical modes are used to represent the energy eigenstates of a quantum harmonic oscillator prepared in a thermal state. The Fourier transform of the work distribution, or the characteristic function, can be obtained by measuring the light intensity at the output of a properly designed interferometer. The usefulness of the approach is illustrated by calculating the work distribution for a unitary operation that displaces the linear momentum of the oscillator. Other types of processes and quantum systems can be implemented with the same scheme. We also show that the setup can be used to investigate the energy distribution for open dynamics described by completely positive maps. We discuss the feasibility of the experiment, which can be realized with simple linear optical components.

DOI
10.1103/physreva.94.042305

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We present a proposal of a setup to measure the work distribution of a process acting on a quantum system emulated by the transverse degrees of freedom of classical light. Hermite-Gaussian optical modes are used to represent the energy eigenstates of a quantum harmonic oscillator prepared in a thermal state. The Fourier transform of the work distribution, or the characteristic function, can be obtained by measuring the light intensity at the output of a properly designed interferometer. The usefulness of the approach is illustrated by calculating the work distribution for a unitary operation that displaces the linear momentum of the oscillator. Other types of processes and quantum systems can be implemented with the same scheme. We also show that the setup can be used to investigate the energy distribution for open dynamics described by completely positive maps. We discuss the feasibility of the experiment, which can be realized with simple linear optical components.
Non-equilibrium thermodynamics and quantum information theory are interrelated research fields witnessing an increasing theoretical and experimental interest. This is mainly due to the broadness of these theories, which found applications in many different fields of science, ranging from biology to the foundations of physics. Here, by employing the orbital angular momentum of light, we propose a new platform for studying non-equilibrium properties of high dimensional quantum systems. Specifically, we use Laguerre-Gaussian beams to emulate the energy eigenstates of a two-dimension quantum harmonic oscillator having angular momentum. These light beams are subjected to a process realized by a spatial light modulator and the corresponding work distribution is experimentally reconstructed employing a two-point measurement scheme. The Jarzynski fluctuation relation is then verified. We also suggest the realization of Maxwell's demon with this platform.
Most of the experimental interferometric setup are based on the Mach-Zehnder geometry. Usually in the experimental configurations the photons travel in air, at a speed v independent of λ. An integrated optics approach appears necessary both for practical applications and because it can be useful for fundamental optics studies because the transmitted photons are in a spatial coherent state. We exploited a hybrid setup integrating optical fibres and monolithic optical waveguides to implement an asymmetric nonlinear Mach-Zehnder Interferometer (ANLI). One arm of the interferometer was equipped with a single mode Er:LiNbO3 waveguide, acting as nonlinear component whereas the other arm was an undoped LiNbO3 single mode waveguide, used to obtain a phase shift through the application of a voltage ramp. We injected in the ANLI a 980 nm laser radiation to collect interferograms that could be ascribed exclusively to the pump photons, as all frequency conversion events are localized only in one arm of the interferometer. The Fourier Transform analysis of the experimental data allowed us to perform a n Interaction-Free Quantum Optics experiment. This is a novel approach that can be used because in quantum mechanics the wave functions of a state, expressed in terms of two conjugate variables, are Fourier Transform pairs. In fact, operating in the Fourier Transform time-frequency space-domain, we recovered the spectral composition, in the wavenumber space-domain, of the photons generated by the excitation of an Er3+ doped crystal placed in one arm of the interferometer.
Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to realize an adaptable scheme for learning unitary operations. Our approach borrows from concepts in variational quantum computing, where a search or optimization problem is mapped onto the task of finding a minimum ground state energy for a given energy/goal function. We achieve this by a pseudo-random walk procedure over the parameter space of the unitary operation, implemented with optical matrix-vector multiplication enacted on arrays of Gaussian modes by exploiting the partial Fourier transforming capabilities of a cylindrical lens in the transverse degree of freedom for the measurement. We outline the concept theoretically, and experimentally demonstrate that we are able to learn optical unitary matrices for dimensions d = 2, 4, 8, and 16 with average fidelities of >90%. Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.
We propose an interferometric setting for the ancilla-assisted measurement of the characteristic function of the work distribution following a time-dependent process experienced by a quantum system. We identify how the configuration of the effective interferometer is linked to the symmetries enjoyed by the Hamiltonian ruling the process and provide the explicit form of the operations to implement in order to accomplish our task. We finally discuss two physical settings, based on hybrid optomechanical-electromechanical devices, where the theoretical proposals discussed in our work could find an experimental demonstration.
We review the use of an external auxiliary detector for measuring the full distribution of the work performed on or extracted from a quantum system during a unitary thermodynamic process. We first illustrate two paradigmatic schemes that allow one to measure the work distribution: a Ramsey technique to measure the characteristic function and a positive operator valued measure (POVM) scheme to directly measure the work probability distribution. Then, we show that these two ideas can be understood in a unified framework for assessing work fluctuations through a generic quantum detector and describe two protocols that are able to yield complementary information. This allows us also to highlight how quantum work is affected by the presence of coherences in the system’s initial state. Finally, we describe physical implementations and experimental realisations of the first two schemes.
In this work, we experimentally investigate the classical-light emulation of different notions of nonclassicality in the simplest scenario. We implement this prepare-and-measure scenario involving four preparations and two binary-outcome measurements using two distinct experimental setups that exploit different degrees of freedom of light: polarization and first-order Hermite-Gaussian transverse modes. We additionally model experimental noise through an all-optical setup that reproduces the operational effect of a depolarizing channel. Our experimental results are consistent with the findings of Khoshbin et al. [Phys. Rev. A 109, 032212 (2024)]: under the assumption that the two measurements performed form a tomographically complete set, the observed statistics violate their noise-robust inequalities, indicating inconsistencies with preparation noncontextuality and bounded ontological distinctness for preparations. Although our implementation uses classical light, it reproduces the statistics predicted for the simplest scenario. Since the states and measurements of this scenario underpin computational advantages in tasks such as two-bit quantum random access codes -- among the simplest communication primitives enabling semi-device-independent certification of nonclassicality -- our implementation is directly relevant for such applications.