An Intrinsic Limit to Quantum Coherence due to Spontaneous Symmetry Breaking

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is $t_{\mathrm{spon}}\simeq 2\pi N\hslash /(k_{B}T)$, given in terms of the number of microscopic degrees of freedom $N$, temperature $T$, and the constants of Planck ($\hslash$) and Boltzmann ($k_B$).

Figure 1

Semiclassical time evolution of a two spin qubit that at $t=t_0$ starts interacting with a Lieb-Mattis measurement machine. Quantum coherence is preserved at all times.

Figure 2

Energy level scheme with the zero and two-magnon states, each with its tower of thin spectrum states. The level spacing in the thin spectrum is $E_{\mathrm{thin}}$; magnons live on an energy scale $J$.

Figure 3

The time dependence of the entanglement between states $|0⟩$ and $|2⟩$, $|{\rho }^{\mathrm{OD}}|$, for different numbers of spins $N$ at $T=10\mathrm{K}$ and $t_{\mathrm{rec}}/t_{\mathrm{spon}}={10}^3$. In the bottom figure the decoherence time due to spontaneous symmetry breaking $t_{\mathrm{spon}}$ and the recurrence time $t_{\mathrm{rec}}$ are indicated.