Quantum decoherence of an anharmonic oscillator monitored by a Bose-Einstein condensate

The dynamics of a quantum anharmonic oscillator whose position is monitored by a Bose-Einstein condensate trapped in a symmetric double well potential is studied. The (nonexponential) decoherence induced on the oscillator by the measuring device is analyzed. A detailed quasiclassical and quantum analysis is presented. In the first case, for an arbitrary initial coherent state, two different decoherence regimes are observed: an initial Gaussian decay followed by a power law decay for longer times. The characteristic time scales of both regimes are reported. Analytical approximated expressions are obtained in the full quantum case where algebraic time decay of decoherence is observed.

Figure 1

Graphical representation of an atom chip that can be a realization of the model studied in this work. An array of wires is used to create two dimple traps that contain atoms (red). The traps are separated by tunable barriers. The yellow arrows indicate the currents used to create the traps. On top of the wire configuration that supports the traps, the cantilever (blue) is mounted with a tip (orange) that interacts with the atoms. The figure is inspired by the work [3].

Figure 2

Decay of the expectation value of position and some Wigner functions of the oscillator at different times.

Figure 3

Comparison between the quasiclassical solution (36) (orange line) and the exact numerical solution of the equations of motion (blue line) in the perturbative regime ($\beta x_0^2/2m{\omega }_0^2=0.133$) for an initial coherent state with $x_0=3$, $p_0=0$, ${\omega }_0=1.3$, $\beta =0.05$, and ${\Delta }_{\phi }=0.1$ (atomic units are used).

Figure 4

Mean value of position as a function of ${\omega }_{0}t$ (normalized to its initial value) for an initial state of the oscillator $|\psi \left(0\right)\rangle =\left(1+i\right)|{\psi }_0\rangle /\sqrt{3}+i|{\psi }_1\rangle /\sqrt{3}$. Numerical result (solid line) and the analytical approximation given by Eq. (45) (dashed line) are almost indistinguishable in the figure. Frequency and amplitude of the signal are described with great accuracy by the analytical expression. The envelope of the analytical approximation in Eq. (46) is shown for reference (dotted line). The inset shows the details of the evolution for the expectation value of position in the large time region. $\beta =0.05$, ${\omega }_0=1.3$, ${\Delta }_{\phi }=0.7$ (a.u.).