Greg Dmochowski

Observation of the nonlinear phase shift due to single post-selected photons

Using post-selection and electromagnetically induced transparency in a cold atomic gas it is now possible to generate a strong nonlinear interaction between two optical beams, bringing nonlinear optics into the quantum regime. Over the past years, much effort has gone towards generating interactions between two optical beams so strong that they could be observed at the level of individual photons1,2,3. Interactions this strong, beyond opening up a new regime in optics4, could lead to technologies such as all-optical quantum information processing5,6. However, the extreme weakness of photon–photon scattering has hindered any attempt to observe such interactions at the level of single particles. Here we present an implementation of a strong optical nonlinearity using electromagnetically induced transparency7, and a direct measurement of the resulting nonlinear phase shift for single post-selected photons. We show that the observed phase shift depends not only on the incident intensity of the (coherent-state) input signal, but also in a discrete fashion on whether 0 or 1 photons are detected at the output. We believe that this constitutes the first direct measurement of the cross-phase shift due to single photons, whose presence or absence is established based on a discrete detection event. It opens a door to future studies of nonlinear optics in the quantum regime, and potential applications in areas such as quantum information processing.

Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime.

We present an experiment using a sample of laser-cooled Rb atoms to show that cross-phase modulation schemes continue to benefit from electromagnetically induced transparency (EIT) even as the transparency window is made narrower than the signal bandwidth (i.e., for signal pulses much shorter than the response time of the EIT system). Addressing concerns that narrow EIT windows might not prove useful for such applications, we show that while the peak phase shift saturates in this regime, it does not drop, and the time-integrated effect continues to scale inversely with EIT window width. This integrated phase shift is an important figure of merit for tasks such as the detection of single-photon-induced cross-phase shifts. Only when the window width approaches the systems dephasing rate γ does the peak phase shift begin to decrease, leading to an integrated phase shift that peaks when the window width is equal to 4γ.We present an experiment using a sample of laser-cooled Rb atoms to show that cross-phase modulation schemes continue to benefit from electromagnetically-induced transparency (EIT) even as the transparency window is made narrower than the signal bandwidth (i.e., for signal pulses much shorter than the response time of the EIT system). Addressing concerns that narrow EIT windows might not prove useful for such applications, we show that while the peak phase shift saturates in this regime, it does not drop, and the time-integrated effect continues to scale inversely with EIT window width. This integrated phase shift is an important figure of merit for tasks such as the detection of single-photon-induced cross phase shifts.

Short-pulse cross-phase modulation in an electromagnetically-induced-transparency medium

Electromagnetically induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. This enhancement grows as the transparency window width,

How a Single Photon Can Act Like Many Photons

{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}

Observation of the Nonlinear Phase Shift Due to Single Post-Selected Photons

, is narrowed. Decreasing

Weak-value amplification of low-light-level cross phase modulation

{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}

Increasing the giant Kerr effect by narrowing the EIT window beyond the signal bandwidth

, however, has been shown to increase the response time of the nonlinear medium. This suggests that, for a given pulse duration, the nonlinearity would diminish once the window width became narrower than this pulse bandwidth. We show that this is not the case: the peak phase shift saturates but does not decrease. We show that in the regimes of most practical interest---narrow EIT windows perturbed by short signal pulses---the enhancement offered by EIT is not only in the magnitude of the nonlinear phase shift but also in its increased duration. That is, for the case of signal pulses much shorter (temporally) than the inverse EIT bandwidth, the narrow window serves to prolong the effect of the passing signal pulse, leading to an integrated phase shift that grows linearly with

Increasing The Giant Kerr Effect By Narrowing The EIT Window Beyond The Signal Bandwidth

1/{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}

Weak-value amplification of the nonlinear effect of a single photon

; this continued growth of the integrated phase shift improves the detectability of the phase shift, in principle, without bound. For many purposes, it is this detectability which is of more interest than the absolute magnitude of the peak phase shift. We present analytical expressions based on a linear time-invariant model that accounts for the temporal behavior of the cross-phase modulation for several parameter ranges of interest. We conclude that in order to optimize the detectability of the EIT-based cross-phase shift, one should use the narrowest possible EIT window and a signal pulse that is as broadband as the excited-state linewidth and detuned by half a linewidth.

How the Result of Counting One Photon Can Turn Out to Be a Value of 8

The weak nonlinear effect of a single photon on a probe beam is amplified by postselecting on a rare final state (