Matin Hallaji

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.

How a Single Photon Can Act Like Many Photons

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

Observing the Onset of Effective Mass

The response of a particle in a periodic potential to an applied force is commonly described by an effective mass, which accounts for the detailed interaction between the particle and the surrounding potential. Using a Bose-Einstein condensate of (87)Rb atoms initially in the ground band of an optical lattice, we experimentally show that the initial response of a particle to an applied force is in fact characterized by the bare mass. Subsequently, the particle response undergoes rapid oscillations and only over time scales that are long compared to those of the interband dynamics is the effective mass observed to be an appropriate description. Our results elucidate the role of the effective mass on short time scales, which is relevant for example in the interaction of few-cycle laser pulses with dielectric and semiconductor materials.

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

We implement a strong optical nonlinearity using electromagnetically-induced transparency in cold atoms, and measure the resulting nonlinear phase shift for postselected photons. We believe that this represents the first direct measurement of the cross-phase shift due to individual photons.

Observing the onset of effective mass of a Bose-Einstein condensate in an optical lattice

Here, we report on the first experimental observation of effective mass dynamics using a Bose-Einstein condensate of Rubidium-87 atoms initially in the ground band of an optical lattice. By studying the response of the particles to an abruptly applied force, we show that, while the long-time behaviour is described by the effective mass, the initial response is indifferent to the presence of the lattice. Our results represent an important contribution towards a full understanding of the ultrafast response of electrons in a solid, relevant for example in the interaction of few-cycle laser pulses with dielectric and semiconductor materials.

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

We report on our experimental progress towards observing weak-value amplification of low-light-level cross-phase modulation which will be the first observation of a weak measurement relying on true entanglement between distinct systems.

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

We experimentally show that giant EIT-based Kerr nonlinearities may make use of EIT windows narrower than the signal bandwidth, allowing for experiments with short signal pulses to benefit from this enhancement, e.g. for QND measurements.

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

We experimentally show that giant EIT-based Kerr nonlinearities continue to benefit from narrowing the EIT window even as the signal bandwidth comes to exceed this transparency width