Photon Measurement

Ghasem Naeimi, Siamak Khademi, Ozra Heibati

Measurement of photons number in a quantum cavity is very difficult and the photons number is changed after each measurement. Recently, many efforts have been done for the nondemolition measurement methods. Haroche et al. succeed in recognizing existence or nonexistence of one photon in a quantum cavity. In this paper, we employ their experimental setup for a quantum nondemolition measurement and pump a coherent state in their quantum cavity. In this case, we could detect more photons in the quantum cavity by a measurement of a displaced Wigner function. It is also shown that the measurement of more than one photon is possible by the Haroche method by measuring just one point of displaced Wigner function. Furthermore, if the cavity field is filled by a superposition of two number states, the average number of photons within the cavity would be measurable. We show that their setup is also suitable to apply for the measurement of the squeezing parameter for the squeezed state of photons number in the quantum cavity successfully.

Crispin W. Gardiner, P. Zoller

Yinnon Glickman, Shlomi Kotler, Nitzan Akerman +1 more

After measurement, a wave-function is postulated to collapse on a predetermined set of states--the measurement basis. Using quantum process tomography, we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion after spontaneous photon scattering and detection. This basis is determined by the excitation laser polarization and the direction along which the photon was detected. Quantum tomography of the combined spin-photon state reveals that although photon scattering entangles all superpositions of the measurement-basis states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings shed light on the process of quantum measurement in atom-photon interactions.

Crispin W. Gardiner

Sofiane Merkouche, Valérian Thiel, Brian J. Smith

Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process affects a generalized measurement on the input two-photon state. We describe the positive operator-valued measure (POVM) associated with such a measurement and show that its elements are proportional to the two-photon states produced by the time-reversed PDC process. Such a detection acts as a joint measurement on two photons and is thus an important component of many quantum information processing protocols relying on photonic entanglement. Using the retrodictive approach, we analyze the properties of the two-photon POVM that are relevant for quantum protocols exploiting two-photon states and measurements.

Joachim Piprek