Nonlinear behavior of geometric phases induced by photon pairs

Abstract

In this study, we observe the nonlinear behavior of the two-photon geometric phase for polarization states using time-correlated photons pairs. This phase manifests as a shift of two-photon interference fringes. Under certain arrangements, the geometric phase can vary nonlinearly and become very sensitive to a change in the polarization state. Moreover, it is known that the geometric phase for $N$ identically polarized photons is $N$ times larger than that for one photon. Thus, the geometric phase for two photons can become two times more sensitive to a state change. This high sensitivity to a change in the polarization can be exploited for precision measurement of small polarization variation. We evaluate the signal-to-noise ratio of the measurement scheme using the nonlinear behavior of the geometric phase under technical noise and highlight the practical advantages of this scheme.Comment: 10 pages, 10 figure

Observation of nonlinear variations in a three-vertex geometric phase in a two-photon polarization qutrit

“…Even in this condition, the measured average power of the interference fringes is 1.1 pW, which corresponds to 2.1 × 10 6 photons/s. This output power is three orders of magnitude greater than that in previous experiments [25][26][27]. • .…”

“…Moreover, coincidence counting of photon pairs is not needed in the time-reversed two-photon interferometer; therefore, we can measure the geometric phase in two-photon polarization using a simpler setup. Indeed, this technique cannot be used for observing the nonclassical effect of photon pairs [25,27] because the technique is implemented using classical light. However, for the purpose of this study, that is, to verify that the geometric phases in a two-photon polarization qutrit change as predicted by the Bloch sphere representation, this technique is more advantageous than the conventional method using a two-photon interferometer.…”

“…Such measurements have typically been made using a two-photon interferometer [25][26][27]. In the two-photon interferometer, we need to generate photon pairs by spontaneous parametric down-conversion (SPDC) and to detect them by coincidence counting.…”

“…In the experiment, we measure the three-vertex geometric phase using a quantum eraser [13,25]. Let us consider the interferometer of a photon pair shown in Fig.…”

“…We use a time-reversed two-photon interferometer [24] for the measurement. Unlike the typical method of measuring the geometric phase in two-photon polarization [25][26][27], our setup can obtain vastly more intense signals and can be implemented using classical light. This paper is organized as follows.…”