  In this paper we ask a common psychological question and provide a physics
answer: "Looking into a mirror can one get entangled with one's image?" This is
not a frivolous question; rather, it bears on the effect of boundaries on the
behavior of quantum entanglement between a harmonic oscillator and a quantum
field, a basic problem of interest in proposed mirror-field superposition and
related experiments in macroscopic quantum phenomena, as well as atomic
fluctuation forces near a conducting surface.
  The object's internal degree of freedom is modeled by a harmonic oscillator
and the presence of a perfectly reflecting mirror enforces the Dirichlet
boundary conditions on the quantum field, restricting the latter to a half
space. By assuming a bilinear oscillator-field interaction, we derive a coupled
set of equations for the oscillator's and the field's Heisenberg operators. The
former can be cast in the form of a quantum Langevin equation, where the
dissipation and noise kernels respectively correspond to the retarded and
Hadamard functions of the free quantum field in half space.
  We use the linear entropy as measures of entanglement between the oscillator
and the quantum field under mirror reflection, then solve the early-time
oscillator-field entanglement dynamics and compare it with that between two
inertial oscillators in free space. At late times when the combined system is
in a stationary state, we obtain exact expressions for the oscillator's
covariance matrix and show that the oscillator-field entanglement decreases as
the oscillator moves closer to the mirror. We explain this behavior
qualitatively with the help of a mirror image and provide an answer to the
question raised above. We also compare this situation with the case of two real
oscillators and explain the differences.
