Cross Modulation of Two Laser Beams at the Individual-Photon Level

Abstract

Deterministic photon-photon interactions are a long-standing goal in optical science. Using an atomic ensemble inside a cavity, we demonstrate the mutual cross modulation of two continuous light beams at the level of individual photons. The originally uncorrelated beams derived from independent lasers become anticorrelated, as evidenced by an equal-time cross-correlation function g ð2Þ ¼ 0.89ð1Þ, showing that one photon in one beam extinguishes a photon in the other beam with a probability of 11(1)%. With further technical improvements, our approach should enable the nondestructive continuous detection of traveling optical photons.

Partially Nondestructive Continuous Detection of Individual Traveling Optical Photons

“…Previously, a single-photon transistor was realized using an atomic ensemble inside a high finesse cavity where one stored photon blocked the transmission of more than one cavity photon and could still be retrieved [5]. Such strong cross-modulation [20] can be used for all-optical destructive detection of the stored optical photon, but the parameters in that experiment did not allow nondestructive detection with any appreciable efficiency. High-efficiency pulsed nondestructive optical detection has recently been achieved using a single atom in a cavity [21].…”

Coherent-state-induced transparency

“…In our scheme the control field not only induces transparency for the quantum probe pulse, but simultaneously imparts on the latter a phase shift at the level of few photons via the Kerr-type nonlinear interaction between the two fields. This is fundamentally different from most studies of cross-phase shifts of quantum light, which are based on N -type EIT medium [15,[24][25][26][27], where the Kerr interaction between the signal and probe fields is mediated by a strong classical field. The measurement of the phase shift induced by the control field on the single-photon probe pulse provides nondestructive detection of the number of control photons, thus enabling the quantum nondemolition measurement of the photon number [28] in the control beam.…”

“…This immediately follows also from Eq. (15), where the function 1 F 1 and the exponential factor tend to unity for |α| 2 /N 2 < 1, while for the transparency one needs D ≪ 1 as seen from Eqs. (17).…”

“…From the structure of the Fock-state dependence in Eq. (15) we recognize that the total contribution to the EIT coming from all the modes with a given number of photons k is determined by the term GN 2 k in the denominator of the right hand side of the first equation of (15) indicating that the greater transparency is expected for larger k. However, for fixed |α| 2 and large N 2 , the transparency is induced mainly by the lower Fock states with small number of photons k ∼ 1, because the probability distribution of Fock-states in D is defined by the k-th degree of the mean photon number per mode (|α| 2 /N 2 ) k , which quickly decreases with increasing k. Moreover, the probe field experiences huge absorption, when the control field is in the vacuum state k = 0. As a result, the EIT peak decreases as N 2 increases by the law shown in Fig.3.…”

“…Since its first experimental observation in strontium vapors [2], it has been thoroughly investigated in different material systems including quantum dots [3], quantum wells [4], nanoplasmonics [5], metamaterials [6], and optomechanical systems [7]. Many applications of EIT, ranging from reversible mapping of light-matter states in quantum memory [8][9][10] to all-optical switching of one beam by another [11][12][13] and cross-coupling nonlinearities at the few-photon level [14,15], reveal its ability as a basic tool for implementation of quantum information processing. However, to date, only classical fields are employed in usual EIT schemes to yield transparency in probe light absorption, while, despite the fundamental importance, the transparency induced in atomic ensembles by quantum fields has not been explored yet, except for the cavity-based EIT, where the classical control beam is replaced by a cavity vacuum field [16].…”