Generation of Macroscopic Superpositions of Quantum States by Linear Coupling to a Bath

We demonstrate through an exactly solvable model that collective coupling to any thermal bath induces effectively nonlinear couplings in a quantum many-body (multispin) system. The resulting evolution can drive an uncorrelated large-spin system with high probability into a macroscopic quantum-superposition state. We discuss possible experimental realizations.

Figure 1

Bath-induced formation of a MQS state. (a) A collective (large) spin naturally evolves in the bath into a MQS state. The system is a spin ensemble composed of $N=50$ particles coupled to an Ohmic bath. The cutoff frequency ${\omega }_c$ is chosen such that the collective coupling of the spin ensemble to the bath $\eta =\sqrt{\sum _k{\eta }_k^2}\sim 0.005{\omega }_c$. (b) The coupling spectrum of an Ohmic bath. (c) The time-dependent functions responsible for the nonlinear Lamb shift [$f(t)$] and decoherence [$\Gamma (t)$] dynamics of the system. (d),(e) The absolute value of the density matrix elements $|{\rho }_{m{m}^{\prime }}(t)|$ in the $L_x$ basis [Eq. (4)] at various times. The initial state of the ensemble is a spin coherent state, $|\theta =\pi /4,\varphi =0⟩$, in the $L_x$ basis. The presence of the $|\pm N/2⟩⟨\mp N/2|$ off-diagonal elements (left- and rightmost peaks) signifies the formation of such a state with high fidelity.

Figure 2

Interaction with a cavity mode. As in Fig. 1, for a cavity with a Lorentzian coupling spectrum with width ${\omega }_c$ centered at $10{\omega }_c$. (a) The $f(t)$ and $\Gamma (t)$ functions. (b) The formation of macroscopic quantum superposition for a cavity with a Lorentzian line shape at ${\tau }_{\mathrm{MQS}}={10}^2/{\omega }_c$.