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We demonstrate the simultaneous propagation of slow- and fast-light optical pulses in a four-wave mixing scheme using warm potassium vapor. We show that when the system is tuned such that the input probe pulses exhibit slow-light group velocities and the generated pulses propagate with negative group velocities, the information velocity in the medium is nonetheless constrained to propagate at, or less than, c. These results demonstrate that the transfer and copying of information on optical pulses to those with negative group velocities obeys information causality, in a manner that is reminiscent of a classical version of the no-cloning theorem. Additionally, these results support the fundamental concept that points of non-analyticity on optical pulses correspond to carriers of new information., 11 pages, 6 figures

Although it is widely accepted that classical information cannot travel faster than the speed of light in vacuum, the behavior of quantum correlations and quantum information propagating through actively-pumped fast-light media has not been studied in detail. To investigate this behavior, we send one half of an entangled state of light through a gain-assisted fast-light medium and detect the remaining quantum correlations. We show that the quantum correlations can be advanced by a small fraction of the correlation time while the entanglement is preserved even in the presence of noise added by phase-insensitive gain. Additionally, although we observe an advance of the peak of the quantum mutual information between the modes, we find that the degradation of the mutual information due to the added noise appears to prevent an advancement of the leading edge. In contrast, we show that both the leading and trailing edges of the mutual information in a slow-light system can be significantly delayed.

In this manuscript, we demonstrate the ability of nonlinear light-atom interactions to produce tunably non-Gaussian, partially self-healing optical modes. Gaussian spatial-mode light tuned near to the atomic resonances in hot rubidium vapor is shown to result in non-Gaussian output mode structures that may be controlled by varying either the input beam power or the temperature of the atomic vapor. We show that the output modes exhibit a degree of self-reconstruction after encountering an obstruction in the beam path. The resultant modes are similar to truncated Bessel-Gauss modes that exhibit the ability to self-reconstruct earlier upon propagation than Gaussian modes. The ability to generate tunable, self-reconstructing beams has potential applications to a variety of imaging and communication scenarios., Comment: 8 pages, 4 figures

In this Letter we experimentally demonstrate the generation of squeezed, bright twin beams which arise due to competing gain and absorption, in a medium that is overall transparent. To accomplish this, we make use of a non-degenerate four-wave mixing process in warm potassium vapor, such that one of the twin beams experiences strong on-resonant absorption. At room temperature and above, due to Doppler broadening and smaller frequency detunings compared to other schemes, the ground state hyperfine splittings used in the present double-$\Lambda$ setup are completely overlapped. We show that despite the resulting significant asymmetric absorption of the twin beams, quantum correlations may still be generated. Our results also demonstrate that the simplified model of gain, followed by loss, is insufficient to describe the amount of quantum correlation resulting from the process., Comment: 6 pages, 5 figures

We present the experimental conversion of a spatially-Gaussian optical mode into a self-healing, approximate Bessel-Gauss mode by a non-collinear, spatially-multimode four-wave mixing process in warm atomic vapor. In addition to the mode conversion, a second, spatially-separate conjugate beam is created in a non-Gaussian mode that mimics that of the resulting converted probe beam. Additionally, we show that these resulting beams exhibit the ability to partially self-heal their mode profiles after encountering an obstacle in their paths. This multi-spatial-mode nonlinear gain platform may thus be used as a new method for all-optically generating pairs of self-healing beams.

The generation of light containing large degrees of orbital angular momentum (OAM) has recently been demon- strated in both the classical and quantum regimes. Since there is no fundamental limit to how many quanta of OAM a single photon can carry, optical states with an arbitrarily high difference in this quantum number may, in principle, be entangled. This opens the door to investigations into high-dimensional entanglement shared between states in superpositions of nonzero OAM. Additionally, making use of non-zero OAM states can allow for a dramatic increase in the amount of information carried by a single photon, thus increasing the information capacity of a communication channel. In practice, however, it is difficult to differentiate between states with high OAM numbers with high precision. Here we investigate the ability of deep neural networks to differentiate between states that contain large values of OAM. We show that such networks may be used to differentiate be- tween nearby OAM states that contain realistic amounts of noise, with OAM values of up to 100. Additionally, we examine how the classification accuracy scales with the signal-to-noise ratio of images that are used to train the network, as well as those being tested. Finally, we demonstrate the simultaneous classification of < 100 OAM states with greater than 70 % accuracy. We intend to verify our system with experimentally-produced classi- cal OAM states, as well as investigate possibilities that would allow this technique to work in the few-photon quantum regime.

We theoretically study the phase sensitivity of an SU(1,1) interferometer with a thermal state and squeezed vacuum state as inputs and parity detection as measurement. We find that phase sensitivity can beat the shot-noise limit and approaches the Heisenberg limit with increasing input photon number., Comment: 7 pages, 6 figures

We demonstrate a new four-wave mixing (4WM) geometry based on structured light. By utilizing near-field diffraction through a narrow slit, the pump beam is asymmetrically structured to modify the phase matching condition, generating multi-mode output in both the spatial and frequency domains. We show that the frequency parameter enables selection of various spatial-mode outputs, including a twin-beam geometry which preserves relative intensity squeezing shared between the two beams. The results suggest that the engineering of atomic states via structured light may provide a pathway to a diverse set of quantum resources based on multi-mode squeezed light., Comment: 5 pages, 7 figures

Although it is widely accepted that information cannot travel faster than the speed of light in vacuum, the behavior of quantum correlations and entanglement propagating through actively–pumped dispersive media has not been thoroughly studied. Here we investigate the behavior of quantum correlations and information in the presence of a nonlinear dispersive gaseous medium. We show that the quantum correlations can be advanced by a small fraction of the correlation time while the entanglement is preserved even in the presence of noise added by phase–insensitive gain. Additionally, although we observe an advance of the peak of the quantum mutual information between the modes, we find that the degradation of the mutual information due to the added noise appears to prevent an advancement of the mutual information’s leading tail. In contrast, we show that both the leading and trailing tails of the mutual information in a slow–light system can be significantly delayed in the presence of four-wave mixing (4WM) and electromagnetically induced transparency.

Four-wave mixing in atomic vapor allows for the generation of multi-spatial-mode states of light containing many pairs of two-mode entangled vacuum beams. This in principle can be used to send independent secure keys to multiple parties simultaneously using a single light source. In our experiment, we demonstrate this spatial multiplexing of information by selecting three independent pairs of entangled modes and performing continuous-variable measurements to verify the correlations between entangled partners. In this way, we generate three independent pairs of correlated random bit streams that could be used as secure keys. We then demonstrate a classical four-party secret sharing scheme as an example for how this spatially multiplexed source could be used., Comment: Accepted in Journal of Modern Optics, 7 pages, 3 figures, 2 tables

Due to its vital role in many quantum information and communication protocols, much theoretical and experi- mental work has been conducted in order to investigate the fundamental properties of entanglement. In this work we describe an experimental investigation into the behavior of continuous-variable entanglement and quantum mutual information upon propagation through slow- and fast-light media. A four-wave mixing process in warm atomic vapor is used to generate an entangled two-mode squeezed vacuum state of light. One of the two modes of the resulting state is then sent through a second four-wave mixing process that is tuned to exhibit either slow- or fast-light properties. The cross-correlation and quantum mutual information shared between the resulting modes is quanti ed, and di erences in their behavior after propagation through slow- and fast-light media are discussed.

We send one half of a bipartite entangled state through a dispersive medium and examine the effects of normal and anomalous dispersion on the quantum entanglement, correlations and arrival time of quantum mutual information.

We report the generation of a squeezed vacuum state of light whose noise ellipse rotates as a function of the detection frequency. The squeezed state is generated via a four-wave mixing process in a vapor of 85Rb. We observe that rotation varies with experimental parameters such as pump power and laser detunings. We use a theoretical model based on the Heisenberg-Langevin formalism to describe this effect. Our model can be used to investigate the parameter space and to tailor the ellipse rotation in order to obtain an optimum squeezing angle, for example, for coupling to an interferometer whose optimal noise quadrature varies with frequency., 7 pages - 7 figures

We investigate the propagation of pre-existing quantum correlations through a fast-light medium with an experiment based on two successive four-wave mixing processes in rubidium vapour.

We recently demonstrated optical pulses with large negative group velocities using a scheme based on four-wave-mixing in rubidium vapor. Both the probe and the generated conjugate pulses can experience anomalous dispersion, and we have demonstrated a maximum group advancement of 64% relative to the input pulse width. The four-wave-mixing scheme allows us to send whole images through a fast light medium, and we have analyzed the arrival of spatially-encoded information in the system. We are currently investigating the transport of quantum correlations that are shared by the probe and conjugate modes when sent through fast light media.

We generate entangled twin beams using four-wave-mixing and investigate the behavior of the quantum correlations when one field is sent through a fast-light medium with anomalous dispersion. We report an advance of 3.7±0.1 ns, marking the realization of a negative temporal delay line for quantum states.

We generate entangled twin beams using four-wave-mixing and investigate its propagation through a negative refractive index medium. Anomalous dispersion is generated near a gain line induced by a pump beam in an atomic vapor.

In this letter we experimentally demonstrate that the signal velocity, defined as the earliest time when a signal is detected above the realistic noise floor, may be altered by a region of anomalous dispersion. We encode information in the spatial degree of freedom of an optical pulse so that the imprinted information is not limited by the frequency bandwidth of the region of anomalous dispersion. We then show that the combination of superluminal pulse propagation and realistic detectors with non-ideal quantum efficiency leads to a speed-up of the earliest experimentally obtainable arrival time of the transmitted signal even with the overall pulse experiencing unity gain. This speed-up is reliant upon non-ideal detectors and losses, as perfect detection efficiency would result in the speed of information being equal to the speed of light in vacuum, regardless of the group velocity of the optical pulses., 5 pages, 3 figures

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 $v_{g}=-\frac{c}{880}$ and $v_{g}=-\frac{c}{2180}$, 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., 9 pages, 4 figures

We generate pairs of superluminal pulses via four-wave mixing. A relative pulse peak advancement of the seed pulses of > 50% is demonstrated. Generated conjugate pulses can propagate with negative group velocities of up to ν g = −1/880c.

We generate superluminal pulses via four-wave-mixing in 85Rb vapor, both for the injected and the generated beam, and imprint images on the pulses and time-resolve the arrival of information in the spatial domain.

We generate superluminal pulses via four-wave-mixing in 85Rb vapor and imprint images on the pulses. This allows us to resolve experimentally the arrival time of the spatial information imprinted on the pulses.

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 $\approx50$\,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., Comment: 5 pages, 4 figures

We experimentally investigate a scheme that exploits the multi-spatial quantum correlations between twin squeezed vacuum beams to resolve the shape of a mask partially obstructing one of the beams.

Four-wave-mixing in hot atomic vapor is a versatile tool for spatially multimode squeezed light generation. We demonstrate multimode behavior for different pump-probe configurations producing either single beam squeezing or twin beams.

We report on the experimental demonstration of an all-optical pi cross-phase modulation jump. By performing a preselection, an optically induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or pi phase shift (with no other possible values). The postselection results in optical loss in the output beam. An input state may be chosen near the resulting phase singularity, yielding a pi phase shift even for weak interaction strengths. The scheme is experimentally demonstrated using a coherently prepared dark state in a warm atomic cesium vapor.

The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal, et al., J. Opt. Soc. Am. B, 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled N00N state (|2,0>+|0,2>)/sqrt{2}. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. The output contains a family of entangled states directly applicable to quantum key distribution. Specific output states allow for the heralded creation of N=4 N00N states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity., 6 pages, 4 figures

By performing a pre-selection, an optically-induced unitary transformation, and then a postselection on the polarization degree of freedom, the phase of the output beam acquires either a zero or π phase shift. The scheme is experimentally demonstrated using a coherently prepared dark-state in a warm atomic cesium vapor.

The study of optical parametric amplifiers (OPAs) has been successful in describing and creating nonclassical light for use in fields such as quantum metrology and quantum lithography [Agarwal et al., J. Opt. Soc. Am. B 24, 2 (2007)]. In this paper we present the theory of an OPA scheme utilizing an entangled state input. The scheme involves two identical OPAs seeded with the maximally path-entangled $\ensuremath{\mid}N00N⟩$ state $(\ensuremath{\mid}2,0⟩+\ensuremath{\mid}0,2⟩)∕\sqrt{2}$. The stimulated amplification results in output state probability amplitudes that have a dependence on the number of photons in each mode, which differs greatly from two-mode squeezed vacuum. A large family of entangled output states are found. Specific output states allow for the heralded creation of $N=4$ $N00N$ states, which may be used for quantum lithography, to write sub-Rayleigh fringe patterns, and for quantum interferometry, to achieve Heisenberg-limited phase measurement sensitivity.

Manipulating the group velocity of light has resulted in many advances, including slowing light to a car’s pace, stopping light and even forcing pulses to propagate faster than the speed of light in a vacuum. While the group velocity is equal to or less than the speed of light in a vacuum (c) when propagating through a medium exhibiting normal dispersion, anomalous dispersion allows the group velocity to be greater than c, or even negative. Strangely, the peak of a pulse propagating with a negative group velocity through a medium appears to exit the medium before entering it. This is a result of interference from spectral components of a pulse propagating with different phase velocities in the medium.

We experimentally demonstrate optical logic “or” and “nor” gates via coherent feedback. Based on a four-wave mixing process in hot rubidium vapor, two feedback beams are capable of fulfilling an optical “nor” gate for the feedback-suppressed state and an optical “or” gate for the feedback-boosted state simultaneously. The logic gates exhibit transition times faster than previously demonstrated in rubidium vapor. Coherent photon conversion between the two logic states, due to the atomic coherence, is observed in the coherent feedback process.

We demonstrate photodetection with single-photon level sensitivity using slow light through a four-wave mixing process with high dispersion and high gain in hot rubidium vapor. The delay times are dependent on the few-photon input states.

We prepare a parametric self-oscillation regime in hot rubidium vapor and observe single-photon level induced ultraslow matched pulses by four-wave mixing. The delay times are dependent on the few-photon input states.