Optical discrimination between spatial decoherence and thermalization of a massive object

We propose an optical ring interferometer to observe environment-induced spatial decoherence of massive objects. The object is held in a harmonic trap and scatters light between degenerate modes of a ring cavity. The output signal of the interferometer permits to monitor the spatial width of the object’s wave function. It shows oscillations that arise from coherences between energy eigenstates and that reveal the difference between pure spatial decoherence and that coinciding with energy transfer and heating. Our method is designed to work with a wide variety of masses, ranging from the atomic scale to nanofabricated structures. We give a thorough discussion of its experimental feasibility.

Figure 1

Setup of the experiment. An atom or a more massive oscillating object, e.g., a nanoparticle, is held in a harmonic potential $\left(P\right)$. An incoming photon is split and “hits” the object from both sides. The source $\left(S\right)$, the beam splitter (BS) and the phase shifter (PS) form a preparation system which ensures that the photon mode is symmetric with respect to the symmetry axis. (PS compensates the phase difference between the reflected and transmitted wave at the beam splitter.) The same system acts as a detection system whereby the antisymmetric photon mode is sent to detector $D$. The potential is symmetric about the symmetry axis as well. If, for example, the object is initially prepared in a state of well defined parity (e.g., the ground state of the potential), its final state will remain a parity eigenstate unless decoherence breaks the initial symmetry of the photon+object system.

Figure 2

Average photon number $N_o\left(t_p\right)$ hitting the odd detector $\left(D\right)$ for $N_{in}={10}^9$ incoming photons, as a function of the delay time $t_p$ in microsecond at which the measurement takes place. In the inset the initial oscillations are magnified. Parameters are given in Table ($\mathrm{Rb}$ atom). The coupling to the environment is taken in the pure decoherence form of Eq. (7). A thermalizing environment [Eq. (8)] would not lead to the superimposed oscillations, but to an otherwise similar behavior.