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Pointer States in the Born-Markov approximation

Uttam Singh, Adam Sawicki, Jarosław K. Korbicz

Abstract

Explaining the emergence of classical properties of a quantum system through its interaction with the environment has been one of the promising ideas on how to understand the notorious quantum-to-classical transition. A pivotal role in this approach is played by, so called, pointer states which are quantum states least affected by the environment and are ``carriers" of classical behavior. We develop here a general method on how to find pointer states. Working within the Born-Markov approximation, we combine methods of group theory and open quantum systems to derive explicit equations describing pointer states. They contain variances squared of certain operators, thus resembling the defining equations of coherent states, but are in general different from the latter. This shows that two notions of being ``the closest to the classical" -- one defined by the uncertainty relations and the other by the interaction with the environment -- are in general different. As an example, we study arbitrary spin-$J$ systems interacting with bosonic or spin thermal environments and find explicitly pointer states for $J=1$.

Pointer States in the Born-Markov approximation

Abstract

Explaining the emergence of classical properties of a quantum system through its interaction with the environment has been one of the promising ideas on how to understand the notorious quantum-to-classical transition. A pivotal role in this approach is played by, so called, pointer states which are quantum states least affected by the environment and are ``carriers" of classical behavior. We develop here a general method on how to find pointer states. Working within the Born-Markov approximation, we combine methods of group theory and open quantum systems to derive explicit equations describing pointer states. They contain variances squared of certain operators, thus resembling the defining equations of coherent states, but are in general different from the latter. This shows that two notions of being ``the closest to the classical" -- one defined by the uncertainty relations and the other by the interaction with the environment -- are in general different. As an example, we study arbitrary spin- systems interacting with bosonic or spin thermal environments and find explicitly pointer states for .
Paper Structure (9 sections, 73 equations, 2 figures)

This paper contains 9 sections, 73 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Pointer states and group-theoretical methods in the Born-Markov approximation.
  3. Quantum Brownian Motion case
  4. Spin-$J$ systems
  5. Conclusions
  6. Spin-1 systems
  7. High temperature regime gdH
  8. Intemediate temperature regime, gdI
  9. Low temperature regime, gdL

Figures (2)

  • Figure 1: Values of the rescaled entropy production $\overline{s}/2D$ for random pure states in the high temperature limit (see Eq. \ref{['spinJht']}) for spin-$1$ system. Each blue dot in the plot corresponds to the value of the rescaled entropy production for a single random pure state. The red dashed horizontal line corresponds to the minimum value of the rescaled entropy production $\overline{s}/2D$ obtained by using spin coherent states. The black horizontal line indicates the true minimum value, $0.4375$, and it is strictly lower than the value obtained for the spin-coherent states.
  • Figure 2: The plot shows value of the function $\overline{s}_{\min}/2D$ for a spin-$1$ system, for various values of $\gamma/D$ that are decided by the temperature of environment. $\gamma/D$ varies from $0$ to $1$ as we decrease temperature.