Correlation engineering via nonlocal dissipation

Open Access

Correlation engineering via nonlocal dissipation

K. Seetharam, A. Lerose, R. Fazio, and J. Marino

Phys. Rev. Research 4, 013089 – Published 3 February 2022

Abstract

Controlling the spread of correlations in quantum many-body systems is a key challenge at the heart of quantum science and technology. Correlations are usually destroyed by dissipation arising from coupling between a system and its environment. Here, we show that dissipation can instead be used to engineer a wide variety of spatiotemporal correlation profiles in an easily tunable manner. We describe how dissipation with any translationally invariant spatial profile can be realized in cold atoms trapped in an optical cavity. A uniform external field and the choice of spatial profile can be used to design when and how dissipation creates or destroys correlations. We demonstrate this control by generating entanglement preferentially sensitive to a desired spatial component of a magnetic field. We thus establish nonlocal dissipation as a route toward engineering the far-from-equilibrium dynamics of quantum information, with potential applications in quantum metrology, state preparation, and transport.

Received 6 February 2021
Accepted 17 December 2021

DOI:https://doi.org/10.1103/PhysRevResearch.4.013089

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Cavity quantum electrodynamics Coherent control Cold atoms & matter waves Cold gases in optical lattices Magnetization dynamics Quantum metrology Quantum optics Quantum state engineering

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

K. Seetharam ^1,2,*, A. Lerose ³, R. Fazio^4,5, and J. Marino^2,6

¹Department of Electrical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
³Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
⁴International Center for Theoretical Physics ICTP, Strada Costiera 11, I-34151 Trieste, Italy
⁵Dipartimento di Fisica, Universita di Napoli “Federico II”, Monte S. Angelo, I-80126 Napoli, Italy
⁶Institut für Physik, Johannes Gutenberg Universität Mainz, D-55099 Mainz, Germany

^*Corresponding author: kis@mit.edu

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Vol. 4, Iss. 1 — February - April 2022

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Images

Figure 1
Experimental realization. Spin degrees of freedom are encoded in the internal states of atoms trapped in a leaky optical cavity. A magnetic field gradient, $\vec{B} (n)$ , and a classical Raman beam, $Ω (t)$ , with multiple sidebands (inset) are used to generate a desired spatial profile, $f (| n - m |)$ , of nonlocal dissipation.
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Figure 2
Dynamical confinement via dissipation. Panels (a)–(c) correspond to a long-range spatial profile with $α = 1.25$ . Panels (d)–(f) correspond to a short-range spatial profile with $χ = 2.0$ . For both cases, we choose $κ = 1$ and initialize the system in a spin coherent state pointing in the direction $θ (t = 0) = 0.4 π$ , $ϕ (t = 0) = 0$ . (a), (d) Motion of the collective spin on the Bloch sphere. (b), (e) Squeezing of the collective spin. (c), (f) Connected correlation function $C^{z z} (r, t)$ . Correlations spread and then contract in accordance to the motion of the collective spin. Upper bounds are imposed on the color scales to visually highlight correlation profiles both here and in Fig. 3; adjacent sites numerically take on values of order $10^{- 2}$ to $10^{- 1}$ .
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Figure 3
Modulating correlations via a uniform field. We initialize the system in a spin coherent state pointing in the direction $θ (t = 0) = 0.4 π$ , $ϕ (t = 0) = 0$ for all panels. (a), (b) Collective spin motion and connected correlation function $C^{z z} (r, t)$ for a long-range spatial profile with $α = 1.25$ . System parameters are $κ = 0.8$ , $ω_{F} = 1.0$ , and $φ = 0.25 π$ . (c), (d) Collective spin motion and connected correlation function $C^{z z} (r, t)$ for a long-range spatial profile with $α = 1.1$ . System parameters are $κ = 0.95$ , $ω_{F} = 1.0$ , and $φ = 0.1 π$ . (e), (f) Squeezing parameter and connected correlation function $C^{z z} (r, t)$ for a short-range spatial profile with $χ = 3.0$ . System parameters are $κ = 1.2$ , $ω_{F} = 1.0$ , and $φ = 0$ .
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Figure 4
Preferentially squeezing a target wave vector. Spatial squeezing parameter for a spatial profile $f_{n, m} = cos (k^{*} | n - m |) e^{- | n - m | / χ}$ with $χ = 50$ and $k^{*} = 0.3 π$ . System parameters are $κ = 0.8$ , $ω_{F} = 1.0$ , and $φ = 0$ . The system is initialized in a spin coherent state pointing in the direction $θ (t = 0) = 0.4 π$ , $ϕ (t = 0) = 0$ . The figure inset shows that the Fourier transform of the spatial profile is peaked around $k^{*}$ .
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Figure 5
Sideband amplitude construction. (a) Sideband amplitudes required to construct a long-range spatial profile $f (| n - m |) = {(| n - m | + 1)}^{- α}$ on a 100-site chain. (b) Spatial profile resulting from the amplitudes in (a). (c) Fourier transform of the long-range spatial profile. (d) Sideband amplitudes required to construct a short-range spatial profile $f (| n - m |) = e^{- | n - m | / χ}$ on a 100-site chain. (e) Spatial profile resulting from the amplitudes in (d). (f) Fourier transform of the short-range spatial profile.
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Figure 6
Crossover between dissipative and coherent dynamics. We compute the correlation function $C^{z z} (r, t)$ for a system whose dynamics is composed of a long-range dissipation channel ( ${\hat{L}}_{n} = {\hat{S}}_{n}^{-}$ ) with strength $κ$ and a long-range spin-exchange Hamiltonian with strength $η$ . For both generators, the spatial profile is $f (| n - m |) = {(| n - m | + 1)}^{- α}$ with $α = 1.25$ . The system exhibits a crossover between $η / κ = 0.25$ and $η / κ = 0.5$ . (a) $κ = 1.0$ , $η = 0.0$ (only dissipation). (b) $κ = 1.0$ , $η = 0.25$ . (c) $κ = 1.0$ , $η = 0.5$ . (d) $κ = 1.0$ , $η = 1.0$ . (e) $κ = 1.0$ , $η = 2.0$ . (f) $κ = 0.0$ , $η = 1.0$ (only Hamiltonian).
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