Strongly-interacting photons
The quest for quantum nonlinearity (strongly-interacting photons)
The realization of strong atom-photon and photon-photon interactions is a long-standing goal of both fundamental and technological significance. Such interactions could be harnessed to interface atomic (stationary) and photonic (flying) qubits, realize deterministic all-optical quantum logic, engineer non-classical states as resources for quantum metrology and sensing, as well as study strongly-interacting many-body physics of photons. However, the interaction between a single atom and a single photon in free space is limited by the ratio of the scattering cross section to the beam size. Due to diffraction limit, the probability to scatter a photon is far below one. The realization of strong photon-photon interaction appears to be even more daunting, as photons usually do not interact with each other at all.
At low optical powers, most optical materials exhibit only linear optical phenomena. An atom or atom-like emitter naturally has nonlinear optical responses, but matching the diffraction-limited photon mode to the interaction cross section poses a great challenge. A highly-successful remedy is to confine the photons in a resonator. We took an alternative route in free space by mapping photons onto collective states of an atomic ensemble--a superposition of the electromagnetic field and collective Raman coherences involving strongly-interacting Rydberg states. The atom-atom interaction is thereby mapped to photon-photon interaction. It is worth noting that, in addition to mediate strong photon interactions, Rydberg-Rydberg interactions have propelled neutral atoms to be a compelling quantum computing platform in recent years.
Rydberg-Rydberg interactions
Rydberg atoms have one or more electron excited to high principal quantum number. Due to the lack of wavefunction overlap, their lifetime (hundreds of microseconds) is much longer than excited states with low principal quantum numbers. Typically, the van der Waals interaction leads to "blockade" within a length scale of a few micrometers. Namely, multiple excitations to the Rydberg state is prohibited because the interaction shifts the state out of resonance. If coupled to degenerate states, the Rydberg atoms experience long-range dipole-dipole interactions, whose result is not an energy shift but "flip-flop" between the coupled states.
Single-photon nonlinearity in the dissipative regime
A quantum probe field incident onto a cold atomic gas is coupled to Rydberg states by means of a second, stronger laser field (control field). For a single incident probe photon, the control field induces a spectral transparency window in the otherwise opaque medium via electromagnetically induced transparency (EIT), and the probe photon travels at much reduced speed in the form of a coupled excitation of light and matter (a Rydberg polariton). If two probe photons are incident onto the Rydberg medium, the strong interaction between two Rydberg atoms tunes the transition out of resonance, thereby destroying the transparency and leading to absorption. To demonstrate that we were operating in a quantum nonlinear regime, we measured the correlation function of the transmitted probe light and observed strong antibunching, largely limited by background light.
Ref
T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin & V. Vuletić
Quantum nonlinear optics with single photons enabled by strongly interacting atoms. Nature 488, 57 (2012)
Featured in News and Views in Nature 488, 39 (2012)
Single-photon nonlinearity in the dispersive regime
We demonstrated a quantum nonlinear medium inside which individual photons travel as massive particles with strong mutual attraction, such that the propagation of photon pairs is dominated by a two-photon bound state. By operating in a dispersive regime away from the intermediate atomic resonance, where atomic absorption is low, we realized a situation in which Rydberg-atom-mediated coherent interactions between individual photons dominate the propagation dynamics of weak light pulses. We measured the dynamical evolution of the two-photon wavefunction using time-resolved quantum state tomography, and demonstrated a conditional phase shift exceeding one radian, resulting in polarization-entangled photon pairs.
Ref
O. Firstenberg, T. Peyronel, Q.-Y. Liang, A. V. Gorshkov, M. D. Lukin & V. Vuletić
Attractive photons in a quantum nonlinear medium. Nature 502, 71 (2013)
Featured in News and Views in Nature 502, 40 (2013)
Photonic trimers
We observed the creation and observation of a traveling three-photon bound state inside a strongly nonlinear optical medium. The photonic trimer, which can be viewed as a quantum soliton, is directly observed via bunching and a strongly nonlinear optical phase. Its size and phase are distinctly different from a two-photon bound state. Our observations thus constituted, to our knowledge, the first observations of such quantum solitons where the optical nonlinearity is so strong that the wave packet shape depends on the constituent number of photons in a quantized manner.
We measured the dynamical evolution of the three-photon wavefunction, and demonstrate a deterministic conditional phase, corresponding to photon trimers whose propagation dynamics are dominated by a three-photon bound state never previously observed. Our measurements can be understood and quantitatively described by a generic quantum field theory. This theory also demonstrates the presence of a substantial effective three-body force that arises from the saturation of the Rydberg interaction. This effective N-body force offers intriguing possibilities to study exotic many-body phases of light and matter, including quantum materials that cannot be realized with conventional systems.
Ref for the experiment
Q.-Y. Liang, A. V. Venkatramani, S. H. Cantu, T. L. Nicholson, M. J. Gullans, A. V. Gorshkov, J. D. Thompson, C. Chin, M. D. Lukin & V. Vuletić
Observation of a three-photon bound state in a quantum nonlinear medium. Science 359, 783 (2018)
Ref for the theory
M. J. Gullans, J. D. Thompson, Y. Wang, Q.-Y. Liang, V. Vuletić, M. D. Lukin, & A. V. Gorshkov
Effective field theory for Rydberg polaritons. Phys. Rev. Lett. 117, 113601 (2016)
Symmetry-protected collisions between a propagating photon and a stored one
All the above projects made use of the van der Waals interaction, while this one switched to the dipole-dipole interaction by transferring the stored photon to a different Rydberg state with opposite parity from the propagating photon. Therefore, the energy does not change if the two photons exchange their Rydberg states.
As the two photons coherently switch places under the dipole–dipole interaction, they acquires a phase shift of exactly π /2 in the process. This phase is analogous to that acquired by a spin-1/2 particle undergoing resonant spin rotation. The half-integer value of the phase shift in units of π is protected by the symmetry of the effective Hamiltonian against variations in the experimental parameters, unlike the phase shift acquired in the dispersive regime using the van der Waals interaction.
A modest extension of this work should allow for a controlled π phase shift quantum gate between two photons, by using microwave control to pass the polaritons through each other a second time before they exit the cloud.
Ref
J. D. Thompson, T. L. Nicholson, Q.-Y. Liang, S. H. Cantu, A. V. Venkatramani, S. Choi, I. A. Fedorov, D. Viscor, T. Pohl, M. D. Lukin & V. Vuletić
Symmetry-protected collisions between strongly interacting photons. Nature 542, 206 (2017)