Detector Models for the Quantum Time of Arrival

Manufacturing time operators: Covariance, selection criteria, and examples

“…Ref. [14] for a review). Indeed, cold atoms and quantum optics offer examples of times of events (other than arrivals), such as jump times, excitation times, escape times, admitting a treatment in terms of covariant observables.…”

“…"Time-of-event", and in particular time-of-arrival operators and probability densities are similar to clock operators (for reviews of this concept see [13,14]). Physically, we expect that a free particle in one dimension will arrive with certainty at a given detection point (including negative times and ignoring the case of zero momentum which is of measure zero for an arbitrary physical wavepacket).…”

Quantum-optical implementation of non-Hermitian potentials for asymmetric scattering

“…for the atom before the first spontaneous emission impinging with wavenumber k in a laser adapted interaction picture, obeys, after applying the rotating wave approximation, an effective stationary Schrödinger equation with a time-independent Hamiltonian [19,33]…”

“…We assume perpendicular incidence of the atom on the laser sheet for simplicity, oblique incidence is treated e.g. in [6,33]. Here E = 2 k 2 /2m is the energy, and Ω(x) is the position-dependent, on-resonance Rabi frequency, where real and imaginary parts may be controlled independently using two laser field quadratures [39]; γ is the inverse of the life time of the excited state; ∆ = ω L − ω 12 is the detuning (laser angular frequency minus the atomic transition angular frequency ω 12 ); K = p 2 /2m is the kinetic energy, p = −i ∂/∂x; and 1 = |1 1| + |2 2| is the unit operator for the internal-state space.…”

“…We start with a two-level atom with ground level |1 and excited state |2 impinging onto a laser illuminated region. For a full account of the model and further references see [33]. The motion is assumed one dimensional, either because the atom is confined in a waveguide or because the direction x is uncoupled to the others.…”