Characterizing two-mode-squeezed light from four-wave mixing in rubidium vapor for quantum sensing and information processing.

We present a study of homodyne measurements of two-mode, vacuum-seeded, quadrature-squeezed light generated by four-wave mixing in warm rubidium vapor. Our results reveal that the vacuum squeezing can extend down to measurement frequencies of less than 1 Hz, and the squeezing bandwidth, similar to the seeded intensity-difference squeezing measured in this system, reaches up to approximately 20 MHz for typical pump parameters. By dividing the squeezing bandwidth into smaller frequency bins, we show that different sideband frequencies represent independent sources of two-mode squeezing. These properties are useful for quantum sensing and quantum information processing applications. We also investigate the impact of group velocity delays on the correlations in the system, which allows us to optimize the useful spectrum.

Pseudo-arbitrary sideband generation by phase modulation calculated with iterative phase retrieval.

A method for arbitrarily tailoring amplitude and phase of sidebands generated with a phase shifting electro-optic modulator (EOM) is presented. The technique is extremely simple experimentally, requiring only a single EOM driven by an arbitrary waveform generator. The required time domain phase modulation is calculated using an iterative phase retrieval algorithm, which takes into account the desired spectrum (both amplitude and phase), and other physical constraints. The algorithm works consistently and finds solutions which accurately recreate the desired spectrum. Since EOMs only modulate phase, the solutions will usually match the desired spectrum over the specified range by redistributing optical power to regions of the spectrum that are unspecified. This basic Fourier limitation is the only in-principle limit to the arbitrariness of the spectrum tailoring. An experimental demonstration of the technique is performed, which shows complex spectra can be generated with high accuracy.

Two-beam coupling in the production of quantum correlated images by four-wave mixing.

We investigate the effect of 2-beam coupling in different imaging geometries in generating intensity-difference squeezing from four-wave mixing (4WM) in Rb atomic vapors. A recently-introduced dual-seeding technique can cancel out the classical noise in a seeded four-wave mixing process. This dual-seeding technique, however, can introduce new complications that involve 2-beam coupling between different seeded spatial modes in the atomic vapor and can ruin squeezing at frequencies on the order of the atomic linewidth and below. This complicates some forms of quantum imaging using these systems. Here we show that seeding the 4WM process with skew rays can eliminate the excess noise caused by 2-beam coupling. To avoid 2-beam coupling in bright, seeded images, it is important to re-image the object in the gain medium, instead of focussing through it.

Signal advance and delay due to an optical phase-sensitive amplifier.

Fast and slow light media exploit a steep frequency dependence in their index of refraction in order to advance or delay a modulated signal. Here we observe a qualitatively similar advance and delay from an optical phase-sensitive amplifier (PSA). Unlike in the case of slow and fast light, this effect is due to a redistribution of power between imbalanced signal sidebands, and the advance or delay is dependent on the optical phase of the input. The PSA adds energy and also changes the frequency spectrum of the input. We show that the advances and delays observed in a PSA implemented using four-wave mixing in a warm rubidium vapor are consistent with the expected behavior of an ideal PSA.

Effect of imperfect homodyne visibility on multi-spatial-mode two-mode squeezing measurements.

We study the effect of homodyne detector visibility on the measurement of quadrature squeezing for a spatially multi-mode source of two-mode squeezed light. Sources like optical parametric oscillators (OPO) typically produce squeezing in a single spatial mode because the nonlinear medium is within a mode-selective optical cavity. For such a source, imperfect interference visibility in the homodyne detector couples in additional vacuum noise, which can be accounted for by introducing an equivalent loss term. In a free-space multi-spatial-mode system imperfect homodyne detector visibility can couple in uncorrelated squeezed modes, and hence can cause faster degradation of the measured squeezing. We show experimentally the dependence of the measured squeezing level on the visibility of homodyne detectors used to probe two-mode squeezed states produced by a free space four-wave mixing process in 85Rb vapor, and also demonstrate that a simple theoretical model agrees closely with the experimental data.

Twin-beam intensity-difference squeezing below 10 Hz.

We report the generation of strong, bright-beam intensity-difference squeezing down to measurement frequencies below 10 Hz. We generate two-mode squeezing in a four-wave mixing (4WM) process in Rb vapor, where the single-pass-gain nonlinear process does not require cavity locking and only relies on passive stability. We use diode laser technology and several techniques, including dual seeding, to remove the noise introduced by seeding the 4WM process as well as the background noise. Twin-beam intensity-difference squeezing down to frequencies limited only by the mechanical and atmospheric stability of the lab is achieved. These results should enable important low-frequency applications such as direct intensity-difference imaging with bright beams on integrating detectors.

Optimized phase sensing in a truncated SU(1,1) interferometer.

Homodyne detection is often used for interferometers based on nonlinear optical gain media. For the configuration of a seeded, "truncated SU(1,1)" interferometer Anderson, et al. [ Phys. Rev. A95, 063843 (2017)] showed how to optimize the homodyne detection scheme and demonstrated theoretically that it can saturate the quantum Cramer-Rao bound for phase estimation. In this work we extend those results by taking into account loss in the truncated SU(1,1) interferometer and determining the optimized homodyne detection scheme for phase measurement. Further, we build a truncated SU(1,1) interferometer and experimentally demonstrate that this optimized scheme achieves a reduction in noise level, corresponding to an enhanced potential phase sensitivity, compared to a typical homodyne detection scheme for a two-mode squeezed state. In doing so, we also demonstrate an improvement in the degree to which we can beat the standard quantum limit with this device.

Improved measurement of two-mode quantum correlations using a phase-sensitive amplifier.

We demonstrate the ability of a phase-sensitive amplifier (PSA) to pre-amplify a selected quadrature of one mode of a two-mode squeezed state in order to improve the measurement of two-mode quantum correlations that exist before degradation due to optical and detection losses. We use four-wave mixing (4WM) in 85Rb vapor to generate bright beams in a two-mode squeezed state. One of these two modes then passes through a second 4WM interaction in a PSA configuration to noiselessly pre-amplify the desired quadrature of the mode before loss is intentionally introduced. We demonstrate an enhancement in the measured degree of intensity correlation and intensity-difference squeezing between the two modes.

Effect of input phase modulation to a phase-sensitive optical amplifier.

Many optical applications depend on amplitude modulating optical beams using devices such as acousto-optical modulators (AOMs) or optical choppers. Methods to add amplitude modulation (AM) often inadvertently impart phase modulation (PM) onto the light as well. While this PM is of no consequence to many phase-insensitive applications, phase-sensitive processes can be affected. Here we study the effects of input phase and amplitude modulation on the output of a quantum-noise limited phase-sensitive optical amplifier (PSA) realized in hot 85Rb vapor. We investigate the dependence of PM on AOM alignment and demonstrate a novel approach to quantifying PM by using the PSA as a diagnostic tool. We then use this method to measure the alignment-dependent PM of an optical chopper which arises due to diffraction effects as the chopper blade passes through the optical beam.

Temporally multiplexed storage of images in a gradient echo memory.

We study the storage and retrieval of images in a hot atomic vapor using the gradient echo memory protocol. We demonstrate that this technique allows for the storage of multiple spatial modes. We study both spatial and temporal multiplexing by storing a sequence of two different images in the atomic vapor. The effect of atomic diffusion on the spatial resolution is discussed and characterized experimentally. For short storage time a normalized spatial cross-correlation between a retrieved image and its input of 88 % is reported.

Stimulated generation of superluminal light pulses via four-wave mixing.

We report on the four-wave mixing of superluminal pulses, in which both the injected and generated pulses involved in the process propagate with negative group velocities. Generated pulses with negative group velocities of up to v(g)=-1/880c are demonstrated, corresponding to the generated pulse's peak exiting the 1.7 cm long medium ≈50 ns earlier than if it had propagated at the speed of light in vacuum, c. We also show that in some cases the seeded pulse may propagate with a group velocity larger than c, and that the generated conjugate pulse peak may exit the medium even earlier than the amplified seed pulse peak. We can control the group velocities of the two pulses by changing the seed detuning and the input seed power.

Demonstration of images with negative group velocities.

We report the experimental demonstration of the superluminal propagation of multi-spatial-mode images via four-wave mixing in hot atomic vapor, in which all spatial sub-regions propagate with negative group velocities. We investigate the spatial mode properties and temporal reshaping of the fast light images, and show large relative pulse peak advancements of up to 64 % of the input pulse width. The degree of temporal reshaping is quantified and increases as the relative pulse peak advancement increases. When optimized for image quality or pulse advancement, negative group velocities of up to v(g)=-c/880 and v(g)=-c/2180, respectively, are demonstrated when integrating temporally over the entire image. The present results are applicable to temporal cloaking devices that require strong manipulation of the dispersion relation, where one can envision temporally cloaking various spatial regions of an image for different durations. Additionally, the modes involved in a four-wave mixing process similar to the present experiment have been shown to exhibit quantum correlations and entanglement. The results presented here provide insight into how to tailor experimental tests of the behavior of these quantum correlations and entanglement in the superluminal regime.

Multi-spatial-mode single-beam quadrature squeezed states of light from four-wave mixing in hot rubidium vapor.

We present experimental results on the generation of multi-spatial-mode, single-beam, quadrature squeezed light using four-wave mixing in hot Rb vapor. Squeezing and phase-sensitive deamplification are observed over a range of powers and detunings near the (85)Rb D1 atomic transition. We observe -3 dB of vacuum quadrature squeezing, comparable to the best single-spatial mode results previously reported using atomic vapors, however, produced here in multiple spatial modes. We confirm that the squeezing is present in more than one transverse mode by studying the spatial distribution of the noise properties of the field.

Single-photon propagation through dielectric bandgaps.

Theoretical models of photon traversal through quarter-wave dielectric stack barriers that arise due to Bragg reflection predict the saturation of the propagation time with the barrier length, known as the Hartman effect. This saturation is sensitive to the addition of single dielectric layers, varying significantly from sub-luminal to apparently super-luminal and vice versa. Our research tests the suitability of photonic bandgaps as an optical model for the tunneling process. Of particular importance is our observation of subtle structural changes in dielectric stacks drastically affecting photon traversal times, allowing for apparent sub- and super-luminal effects. We also introduce a simple model to link HOM visibility to wavepacket distortion that allows us to exclude this as a possible cause of the loss of contrast in the barrier penetration process.

Entangling light in its spatial degrees of freedom with four-wave mixing in an atomic vapor.

The entanglement properties of two beams of light can reside in subtle correlations that exist in the unavoidable quantum fluctuations of their amplitudes and phases. Recent advances in the generation of nonclassical light with four-wave mixing in an atomic vapor have permitted the production and the observation of entanglement that is localized in almost arbitrary transverse regions of a pair of beams. These multi-spatial-mode entangled beams may prove useful for an array of applications ranging from noise-free imaging and improved position sensing to quantum information processing.

Entangled images from four-wave mixing.

Two beams of light can be quantum mechanically entangled through correlations of their phase and intensity fluctuations. For a pair of spatially extended image-carrying light fields, the concept of entanglement can be applied not only to the entire images but also to their smaller details. We used a spatially multimode amplifier based on four-wave mixing in a hot vapor to produce twin images that exhibit localized entanglement. The images can be bright fields that display position-dependent quantum noise reduction in their intensity difference or vacuum twin beams that are strongly entangled when projected onto a large range of different spatial modes. The high degree of spatial entanglement demonstrates that the system is an ideal source for parallel continuous-variable quantum information protocols.

Quantum encounters of the cold kind.

Since the introduction of laser-cooling techniques for neutral atoms in the early 1980s, the study of collisional interactions between atoms and molecules has been extended to the regime of ultracold temperatures. With nanokelvin temperatures now attainable, our ability to probe the interactions, both experimentally and theoretically, has also progressed. Understanding of the subtle and often highly quantum-mechanical effects that are manifest at such low energies has advanced to the point where new precision measurements are matched by highly accurate theoretical calculations. Low-energy phenomena such as Bose-Einstein condensation and the photoassociation of atoms into bound molecules are now accurately described with no free parameters.

Treasure of the Past X: A Spectroscopic Determination of Scattering Lengths for Sodium Atom Collisions.

We report a preliminary value for the zero magnetic field Na (2)S(f = 1, m = - 1) + Na (2)S(f = 1, m = - 1) scattering length, a 1,-1. This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range [Formula: see text] molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (R e = 72 a 0) of the [Formula: see text] potential curve is instrumental in determining a 1,-1 = (52 ± 5) a 0 and a 2.2 = (85 ± 3) a 0, where the latter is for a collision of two Na (2)S(f = 2, m = 2) atoms.

A Spectroscopic Determination of Scattering Lengths for Sodium Atom Collisions.

We report a preliminary value for the zero magnetic field Na 2S(f = 1, m = - 1) + Na 2S(f = 1, m = - 1) scattering length, a1,-1. This parameter describes the low-energy elastic two-body processes in a dilute gas of composite bosons and determines, to a large extent, the macroscopic wavefunction of a Bose condensate in a trap. Our scattering length is obtained from photoassociative spectroscopy with samples of uncondensed atoms. The temperature of the atoms is sufficiently low that contributions from the three lowest partial waves dominate the spectrum. The observed lineshapes for the purely long-range [Formula: see text] molecular state enable us to establish key features of the ground state scattering wavefunction. The fortuitous occurrence of a p-wave node near the deepest point (Re = 72 a0) of the [Formula: see text] potential curve is instrumental in determining a1,-1 = (52 ± 5) a0 and a2,2 = (85 ± 3) a0, where the latter is for a collision of two Na 2S(f = 2, m = 2) atoms.