Session K08: Nonlinear Optics and Spin Squeezing

Theoretical study of early time superradiance for atom clouds and arrays

We present results from a recent publication where we explore conditions for Dicke superradiance in a cloud of atoms by examining the Taylor series expansion of the photon emission rate at t=0. By defining superradiance as an increasing photon emission rate for $t\sim 0$, we calculate the conditions for superradiance for a variety of cases. We investigate superradiance as defined for photon emission into all angles as well as directional superradiance where the photon emission is only detected in a particular direction. Although all of the examples are for two level atoms that are fully inverted at t=0, the publication contains equations for partially inverted two level atoms and for fully inverted multilevel atoms. The publication also contains an algorithm for efficiently evaluating these equations for atom arrays and uses this algorithm to determine superradiance conditions for large atom number, N → ∞. The method used to explore this system was inspired by S. J. Masson and A. Asenjo-Garcia, "Universality of Dicke superradiance in atomic arrays," arXiv preprint arXiv:2106.02042 (2021).   

Two-mode squeezing in cold atomic ensembles

Two-mode quadrature squeezed light is a valuable resource for fundamental quantum entanglement study, quantum teleportation, and quantum metrology. In this work we demonstrate two schemes for two-mode squeezing generation; both schemes are based on two strong laser fields driving transitions in a Λ-type atomic system.

In the first part of work I will overview our theoretical proposal for generation of two-mode squeezed vacuum (TMSV) through dissipation. The two signal modes interacting with the ground-state atomic coherence interfere destructively, creating TMSV with a particular squeezing parameter. The squeezing is defined by the parameters of the medium. Once the TMSV is created it stops evolving while it propagates through the lossy atomic medium.

The second part combines theoretical and experimental research. Making use of cavity-enhanced double-Λ four-wave mixing, we report –3.6 dB of squeezing (after correcting for losses), which is a record for a cold atomic ensemble. Theoretically the system is analyzed in the Heisenberg-Langevin picture. This enables us to build an intuitive and qualitative description of the experiment. Based on agreement between our experimental and theoretical results we propose routes to further increase the squeezing strength.   

Squeezing in a refractive index-enhanced system

We consider a system of two-photon Raman transitions capable of refraction index enhancement while maintaining low absorption. In this system, the interference of the gain and absorption resonances of the probe beam results in interesting photon statistics properties including significant squeezing of the quantum states, of both photon-number and quadrature types, without the use of an explicitly nonlinear material. We investigate the conditions under which this happens.   

Spin squeezing in driven, superradiant gas: an integrated method to describe cooperative effects

Driving a superradiant system can produce spin squeezing. To show this, we introduce an integrated method to describe cooperative radiation in many-body systems, and apply the method to an optically dense gas of two-level atoms. For a non-driven system, physical observables such as superradiant decay rate and the many-body induced broadening scale with the optical depth of the sample. When the gas is driven by an external field, steady states are found, which give rise to spin squeezing in the atoms. Different optical depths and driving strengths are examined in order to find the maximum squeezed state.   

Dicke superradiance in arrays of multilevel atoms

We investigate Dicke superradiance with multilevel atoms. Dicke superradiance is a dissipative many-body phenomenon where excited atoms collectively emit a short intense burst of light. While this is well understood for two-level systems in a cavity, our work involves extended arrays in free space. In previous work, we showed that Dicke superradiance generically occurs for two-level systems in arrays, provided that the distance between them is sufficiently small. Here, we consider atoms that can decay into multiple states and show that a superradiant burst can be emitted on all transitions. We develop constraints on the relative rates of each transition and on the geometry of the atomic ensemble, and show that the intensity emitted in certain directions features a superradiant burst in arrays of large interatomic spacing. Our results provide a guide to explore this many-body phenomenon in state-of-the-art experimental setups.   

Dicke superradiance in ordered lattices: role of geometry and dimensionality.

We investigate the role of dimensionality and geometry on the collective decay of large atomic arrays. A fully inverted ensemble of atoms at a single point is well known emits a short burst of light that initially grows in intensity and photons are emitted in a burst, so-called Dicke superradiance. For mesoscopic systems, the nature of the decay can be characterized from the statistics of the first two photons, which we evaluate in linear time. For 1D arrays, Dicke superradiance occurs due to suppression of decay channels, is bounded, and cannot occur for any atom number above a particular distance.  In 2D and 3D, it occurs due to constructive interference. In 2D, the maximum interatomic distance for it scales sub-logarithmically with atom number, and as a power law for 3D. In contrast to Dicke's original work, we show that superradiance survives in arrays where the smallest interparticle distance is larger than a wavelength.   

Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency

Quantum sensing and quantum information processing use quantum advantages such as squeezedstates that encode a quantity of interest with higher precision and generate quantum correlations tooutperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by aquantum speed limit. Therefore, the degree to which a quantum advantage can be used in practiceis limited by the time needed to create the state relative to the rate of unavoidable decoherence.Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into asqueezed state which can circumvent the time constraint. Here, we create squeezed states of atomicmotion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice.Building on this protocol, we demonstrate rapid quantum amplification of a displacement operatorthat could be used for detecting motion. Our results can speed up quantum gates and enablequantum sensing and quantum information processing in noisy environments.   

Experimental observation of nonclassical correlations in photon pairs generated from an ensemble of pure two-level atoms

We report the experimental verification of nonclassical correlations for an unfiltered spontaneous four-wave-mixing process in an ensemble of cold two-level rubidium atoms, obtaining $R = (1.98\pm0.03) \nleq 1$ for the violation of a Cauchy-Schwarz inequality in the system, confirming theoretical predictions by Du {\it et al.} in 2007. Quantum correlations are observed in a nano-seconds timescale, in the interference between the sidebands dislocated by the detuning to the atomic resonance. They prevail over the noise background coming from Rayleigh scattering from the same optical transition. These correlations are fragile with respect to processes that disturb the phase of the atomic excitation but are robust to variations in number of atoms and to increasing light intensities.   

Phase transition in a nonlinear optical Ising machine

Many optimization problems such as the traveling salesman problem and number partitioning can be usually solved by finding the ground state of the classical spin model. Realizing an optical Ising machine and demonstrating its optical advantage are currently attracting broad attention in optical physics. We have explored the phase transition in a recently engineered nonlinear optical Ising machine. By tuning the nonlinear interaction, we find that the ferromagnetic to paramagnetic phase transition changes from second-order to first-order due to the competition of different types of spin interactions. Our results provide a deeper theoretical understanding of the nonlinear optical Ising machine and its potential application for addressing optimization problems.   

High-order (N=4–6) multiphoton absorption in GaP, ZnSe, GaSe, and ZGP crystals

With the ability to generate few-cycle optical pulses from mode-locked lasers, focused power densities in excess of 100 GW/cm² are easily achievable even at full (~100 MHz) repetition rates using oscillator outputs. The development of ultrafast sources in the mid-infrared range (MIR, λ > 2 μm) made it possible to demonstrate high-field effects, such as the generation of high harmonics in solids, the generation of a multi-octave supercontinuum, and the creation of an ultra-wideband subharmonic frequency combs and single-cycle MIR transient generation via optical rectification. Therefore, it is important to know the behavior of non-linear materials in terms of high-order detrimental effects such as multiphoton absorption. Here we report on our study of high-order multiphoton absorption (MPA) and its anisotropy in four notable mid-infrared χ⁽²⁾ crystals: GaP, ZnSe, GaSe and ZGP using 2.35 µm femtosecond pulses with peak intensity up to 200 GW/cm² in combination with the Z- scan method. We found that, at the intensities used, the nonlinear absorption obeys a perturbation model with multiphoton absorption (MPA) orders from N = 4 to 6, in good agreement with the bandgaps of the crystals. A study of the role of free carrier absorption, performed by increasing the pulse duration from 30 to 70 fs while maintaining a constant peak intensity, showed that, at our intensity levels, free carriers absorb much stronger than would be expected from their linear absorption cross section. Possible mechanisms of this enhanced absorption by free-carriers include highly non-thermalized distribution of carriers within the lowest conduction band combined with field-induced intravalley scattering and direct absorption to higher conduction bands.