Session G8: Quantum and Nonlinear Optics

Dispersive properties of the phase-sensitive amplifier based on four-wave mixing in hot $^{85}$Rb vapor

We investigate the dispersive properties of the phase-sensitive amplifier based on four-wave mixing in hot $^{85}$Rb vapor. We know from previous experiments [U. Vogl, \textit{et al.}, New J. Phys. \textbf{16}, 013011 (2014).] that quantum correlations can be advanced by fast light propagation, and that the noise added by the phase-insensitive amplifier prevents an advancement of entanglement, bounding the leading edge of the quantum correlations. Slow light propagation, however, is capable of producing a time shift in both the leading edge and the maximum of the mutual information. In the case of a phase-sensitive amplifier it is well known that no extra noise will be added given the correct relative phases (e.g. at the maximal amplification and the maximal deamplification) among the inputs. We have observed that the group index has a dependence on the relative input phases, indicating that there exists no dispersion at the maximal amplification or the maximal deamplification, while at some phases in between these two extremes, the dispersion is non-zero. Further exploration of the dispersive properties, quantum noise correlations, and quantum mutual information propagation through a phase-sensitive amplifier will also be discussed.   

Numerical simulations of light propagation in a dense near-resonant gas

We study light propagation in a dense gas numerically by applying classical electrodynamics to a collection of near-resonant atoms regarded as point dipoles. In the limit when the atom density and the wave number of light satisfy $\rho k^{-3}\ge 1$, dipole-dipole interactions may make the system strongly correlated, whereupon the mean-field type approximations underlying traditional electrodynamics of polarizable media become invalid. In a dense homogeneously broadened sample both the Lorentz-Lorenz local-field shift and the cooperative Lamb shift are absent, but a more conventional phenomenology reemerges in both dilute and inhomogeneously broadened samples.   

Forward light scattering from a dense and cold microscopic 87Rb sample

In this paper we report on the near-resonance forward scattering of light in a cold atomic sample of $^{87}$Rb ranging in density from $10^{11}$ to $10^{14}$ atoms/cm$^3$. The sample, initially prepared in a magneto-optical trap, is loaded into a far-off-resonance trap (FORT) with a temperature of $\sim$100 $\mu$K and Gaussian radii of $\sim$3 $\mu$m and $\sim$280 $\mu$m in the transverse and longitudinal directions, respectively. Here the $F=2\to F'=3$ nearly closed hyperfine transition is studied; in this case, far-off-resonance inelastic Raman transitions are weak. The experimental geometry consists of tightly focusing the near-resonance beam through the optically deep region of the FORT and collecting the transmitted light as a function of detuning from resonance. A shift in the spectral distribution of transmitted light is observed as a function of sample density.   

Controling and Matching Group Velocity of a Bichromatic Field in Double-Double Electromagnetically Induced Transparency

Slowing light has valuable applications in optical switching, Quantum optics and optical storage. It also has potential role to enhance the nonlinear response of an optical medium [1], and closely matching group velocities of different pulses can enhance cross-phase modulation [2]. We use temperature-controlled Doppler broadening to control and match group velocities in both transparency windows of a bichromatic probe field in double-double electromagnetically induced transparency [3]. The different dispersion response in the first and second windows to Doppler broadening make it possible to match the group velocity of the probe field in both windows. Our approximate analytical expressions are based on the Lorentzian approximation for group velocity in Doppler-broadened electromagnetically induced transparency, and we validate these expressions by numerical simulation.\\[4pt] [1] L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).\\[0pt] [2] C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, Phys. Rev. Lett. 90, 197902 (2003).\\[0pt] [3] H. Alotaibi and B. Sanders, arXiv:1310.3318 [quant-ph](2013)   

Correlation functions of single atom resonance fluorescence with slow light media

We consider the resonance fluorescence emitted by a single atom as the field passes through a slow light medium in the regime where the bandwidth of the slow light medium is narrower than the full Mollow spectrum of the emitted light. We first consider the second-order (in the field) correlation function and show how to properly account for the bandwidth of the slow-light medium. We then consider a standard Hanbury-Brown Twiss interferometer modified by placing a slow light medium in one arm. The fourth order (in the field) correlation functions that result from properly considering the bandwidth of the slow light medium depend on non-time ordered operators. We demonstrate how to evaluate these correlation functions. By making an assumption about the functional form for the dispersion of the slow medium, we derive an analytic albeit very complex expression for the correlation functions. Adjusting the center frequency of the slow light medium with respect to the atomic frequency allows us to explore the modifications of the correlations function as different components of the Mollow spectrum are delayed by the slow light medium. The results of these numerical simulations will be presented.   

Theoretical analysis of the nonlinear susceptibility of hydrogen atom

The nonlinear refractive index of air and other gases plays an important role in the understanding of the propagation of intense laser pulses in the atmosphere. Using a numerical basis state method $[1]$ we have performed accurate calculations of the nonlinear susceptibility in hydrogen atom. Currently, models of filamentation mainly use perturbative approaches to determine the nonlinear susceptibility. We compare our results from ab-initio calculations of the nonlinear susceptibity with those from a perturbative calculation. The comparison allows us to determine an intensity at which perturbation theory breaks down for these kinds of calculations. \\[0pt] [1] S.H. Chen et al., Phys. Rev. A {\bf 86}, 013410 (2012)   

Non-classical higher-order photon correlations from a solid-state cQED system

We use the third- and fourth-order autocorrelation functions $g^{(3)}(\tau_1,\tau_2)$ and $g^{(4)}(\tau_1,\tau_2,\tau_3)$ to detect the non-classical character of light transmitted through a photonic-crystal nanocavity containing a strongly-coupled quantum dot probed with a train of coherent light pulses. We contrast the observed values of $g^{(3)}(0,0)$ with the conventionally used $g^{(2)}(0)$ and show that in addition to being necessary for detection of two-photon states emitted by a low-intensity source, $g^{(3)}$ provides a more clear indication of the non-classical character of a light source. We also present preliminary data that demonstrates bunching in the fourth-order autocorrelation function $g^{(4)}(\tau_1,\tau_2,\tau_3)$ as the first step toward detecting three-photon states.   

Delayed Higher-Order Optical Nonlinearities in Noble Gases

The role of higher-order Kerr effect (HOKE) in femtosecond laser filamentation is currently at the center of a controversy, as alleged crossover from positive to negative nonlinear refractive index at higher intensities was proposed to cause filament stabilization. Experimental evidence of HOKE crossover or lack thereof is being hotly debated. Motivated by this debate, we report the frequency-dependent nonlinear refractive index coefficients $n_{2}$ and $n_{4}$ for a series of atmospheric-pressure noble gases: helium, neon, argon, krypton, and xenon. The corresponding atomic hyperpolarizability coefficients are obtained via auxiliary static electric field approach developed on the basis of \textit{ab initio} calculations implemented in Dalton program and performed at the CCSD level of theory with t-Aug-cc-PV5Z basis set. The $n_{4}$ index is obtained using the relations between the degenerate six-wave mixing coefficient and some other frequency-dependent second hyperpolarizability coefficients, which can be calculated on the basis of $n_{2\, }$via the auxiliary field approach. For all the investigated gases, the $n_{4}$ indices are found to be positive over the wavelength range 300 nm-1500 nm. This result runs counter to the HOKE crossover hypothesis. The calculated $n_{4}$ indices demonstrate considerable temporal dispersion, which progressively increases from helium to xenon. This feature implies delayed nonlinearity and calls for modifications in current theoretical models of filamentation process.   

Cooperative Lamb shift in a quantum emitter array

Whenever several quantum light emitters are brought in proximity with one another, their interaction with common electromagnetic fields couples them, giving rise to cooperative shifts in their resonance frequency. Such collective line shifts are central to modern atomic physics, being closely related to superradiance on one hand and the Lamb shift on the other. Although collective shifts have been theoretically predicted more than fifty years ago, the effect has not been observed yet in a controllable system of a few isolated emitters. Here, we report a direct spectroscopic observation of the cooperative shift of an optical electric dipole transition in a system of up to eight Sr ions suspended in a Paul trap. We study collective resonance shift in the previously unexplored regime of far-field coupling, and provide the first observation of cooperative effects in an array of quantum emitters. These results pave the way towards experimental exploration of cooperative emission phenomena in mesoscopic systems.   

Electromagnetically induced transparency in 1D open space

We study scattering of photons from a $\Lambda$- or ladder-type three-level emitter (3LE) embedded in a 1D open waveguide. The weak probe photons in the waveguide are coupled to one of the two allowed transitions of the 3LE, and the other transition is driven by a control beam. This system shows electromagnetically induced transparency (EIT) which is accompanied with the Autler-Townes splitting (ATS) at a strong driving by the control beam, and some of these effects have been observed recently. We show that the nature of second-order coherence of the transmitted probe photons near two-photon resonance changes from bunching to antibunching to constant as strength of the control beam is ramped up from zero to a higher value where the ATS appears.