Nonconservative Forces via Quantum Reservoir Engineering

Shanon L. Vuglar, Dmitry V. Zhdanov, Renan Cabrera, Tamar Seideman, Christopher Jarzynski, and Denys I. Bondar

Phys. Rev. Lett. 120, 230404 – Published 7 June 2018

Abstract

A systematic approach is given for engineering dissipative environments that steer quantum wave packets along desired trajectories. The methodology is demonstrated with several illustrative examples: environment-assisted tunneling, trapping, effective mass assignment, and pseudorelativistic behavior. Nonconservative stochastic forces do not inevitably lead to decoherence—we show that purity can be well preserved. These findings highlight the flexibility offered by nonequilibrium open quantum dynamics.

Received 16 November 2016
Revised 27 December 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.230404

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum control Tunneling & traversal time

General Physics

Authors & Affiliations

Shanon L. Vuglar^1,2,3,*, Dmitry V. Zhdanov⁴, Renan Cabrera², Tamar Seideman⁴, Christopher Jarzynski⁵, and Denys I. Bondar^2,6

¹University of Melbourne, Parkville, Victoria 3010, Australia
²Princeton University, Princeton, New Jersey 08544, USA
³John Brown University, Siloam Springs, Arkansas 72761, USA
⁴Northwestern University, Evanston, Illinois 60208, USA
⁵University of Maryland, College Park, Maryland, 20742, USA
⁶Tulane University, New Orleans, Louisiana 70118, USA

^*shanonvuglar@gmail.com

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Issue

Vol. 120, Iss. 23 — 8 June 2018

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Images

Figure 1
Environment-assisted quantum tunneling resembles cycling with an umbrella: the environment action is qualitatively similar to tailwind (headwind) when going uphill (downhill). The net effect is a reduction of the backscattering probability with minimal side effects on the wave packet parameters.
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Figure 2
The transmission probability (a) and purity (b) for a Gaussian atomic wave packet tunneling through a potential barrier in the presence of electron jets [Eqs. (2), (6), (8), and (9)] as a function of electron momentum $p_{0}$ . In each case, the wave packet has initial mean kinetic energy $K_{0} = 0.0068 (a . u .)$ and the potential barrier is $U (x) = 2 K_{0} e^{- x^{2} / 2}$ . The solid blue, dash-dotted red, and dotted green curves correspond to incident electron energy fluctuations $C p_{0} = 5 \times 10^{- 4}$ , $10^{- 3}$ , and $1.5 \times 10^{- 3} (a . u .)$ respectively. The rightmost points of the curves in (b) correspond to the case when inequality (7) turns into equality.
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Figure 3
The spreading in position (a), increase in energy (b), spreading in momentum (c), and decrease in purity (d) for an atomic wave packet initially in the ground state of a harmonic oscillator [ $U (x) = \frac{1}{2} m (0.01 x)^{2}$ ]. The solid blue, dash-dotted red, and dotted green curves correspond to the incident electrons’ energy fluctuations $C p_{0} = 0.05$ , 0.1, and 0.2 (a.u.), respectively. In each case, $p_{0} = 10^{- 4} a . u .$ Results for a free (i.e., $C = 0$ , $U = 0$ ) wave packet (dashed black) are shown for comparison.
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Figure 4
The expectation value of the position as a function of time for a hydrogen atom in a ramp potential $U (x) = 3.2 \times 10^{- 3} x$ a.u. The dotted blue curve depicts the environment-free case. The solid green curve depicts the atom in an environment (10) [ $M = 10 m$ , $C = 0.1$ ] engineered to give an effective mass 10 times the proton mass $m$ . The dynamics of the hydrogen atom with environmentally induced effective mass $M$ coincide with those of an environment-free particle of mass $M$ (dashed black).
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Figure 5
The expectation value of the velocity as a function of time for an electron in a ramp potential $U (x) = - 10^{3} x$ a.u. The dotted blue curve depicts the environment-free case. The solid green curve depicts the electron in an environment (13) ( $C = 20 a . u .$ ) engineered to induce quasirelativistic behavior with the speed of light chosen to be 7% of the speed of light in vacuum. The environmentally induced quasirelativistic behavior coincides with that of an environment-free relativistic electron with Hamiltonian ${\hat{H}}_{rel} = \sqrt{c^{2} {\hat{p}}^{2} + c^{4}} + U (\hat{x})$ ; $c = 10$ (dashed black).
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