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We demonstrate a slow-light augmented unbalanced Mach-Zehnder interferometer (MZI) which can be used to enhance very significantly the sensitivity of measuring the frequency shift in a laser. The degree of enhancement depends on the group index of the slow-light medium, the degree of imbalance between the physical lengths of the two arms of the MZI, and the spectral width of the laser. For a laser based on a high-finesse cavity, yielding a narrow quantum noise limited spectral width, the group index has to be larger than the finesse in order to achieve enhancement in measurement sensitivity. For the reported results, strong slow-light effect is produced by employing electro-magnetically induced transparency via coherent population trapping in a buffer-gas loaded vapor cell of Rb atoms, with a maximum group index of ~1759. The observed enhancement in sensitivity for a range of group indices agrees well with the theoretical model. The maximum enhancement factor observed is ~22355, and much larger values can be obtained using cold atoms for producing the slow-light effect, for example. The sensitivity of any sensor that relies on measuring the frequency shift of a laser can be enhanced substantially using this technique. These include, but are not limited to, gyroscopes and accelerometers based on a conventional ring laser or a superluminal ring laser, and detectors for virialized ultra-light field dark matter. We also show how similar enhancements can be achieved in a slow-light augmented unbalanced Michelson interferometer.

Large momentum transfer (LMT) is an important technique for magnifying the phase shift accumulated in an atom interferometer. Existing approaches to implement Raman-transition-based LMT all involve physically swapping the propagation directions of the two counterpropagating Raman beams repeatedly, which could significantly complicate the experimental system. Here, we demonstrate a simpler approach for Raman-transition-based LMT that does not involve a physical swap of the directions of the Raman beams. In this approach, both Raman beams are retroreflected, and a Doppler shift induced by a bias velocity of the atoms is used to separate the transition frequencies of the two pairs of counterpropagating Raman beams. Therefore, an effective swap of the directions of the Raman beams can be achieved by shifting the relative frequency between the two Raman beams from the resonant frequency of one pair of the Raman beams to that of the other pair. We demonstrate the use of this technique for LMT-augmented accelerometry using atoms released from a magneto-optic trap.

We analyze theoretically the sensitivity of accelerometry and rotation sensing with a point source interferometer employing large momentum transfer (LMT) and present a design of an inertial measurement unit (IMU) that can measure rotation around and acceleration along each of the three axes. In this design, the launching technique is used to realize the LMT process without the need to physically change directions of the Raman pulses, thus significantly simplifying the apparatus. We also describe an explicit scheme for such an IMU.

We describe a generalized algorithm for evaluating the steady-state solution of the density matrix equation of motion, for the pump-probe scheme, when two fields oscillating at different frequencies couple the same set of atomic transitions involving an arbitrary number of energy levels, to an arbitrary order of the harmonics of the pump-probe frequency difference. We developed a numerical approach and a symbolic approach for this algorithm. We have verified that both approaches yield the same result for all cases studied, but require different computation time. The results are further validated by comparing them with the analytical solution of a two-level system to first order. We have also used both models to produce results up to the third order in the pump-probe frequency difference, for two-, three- and four-level systems. In addition, we have used this model to determine accurately, for the first time, the gain profile for a self-pumped Raman laser, for a system involving 16 Zeeman sublevels in the D1 manifold of 87Rb atoms. We have also used this model to determine the behavior of a single-pumped superluminal laser. In many situations involving the applications of multiple laser fields to atoms with many energy levels, one often makes the approximation that each field couples only one transition, because of the difficulty encountered in accounting for the effect of another field coupling the same transition but with a large detuning. The use of the algorithm presented here would eliminate the need for making such approximations, thus improving the accuracy of numerical calculations for such schemes.

We show that the frequency of a Raman laser is highly correlated or anti-correlated with the frequency of the Raman pump laser, depending on whether the dispersion experienced by the Raman laser is positive or negative. For a subluminal laser, corresponding to a positive dispersion with a group index that is much larger than unity, the shift in its frequency is approximately the same as that in the Raman pump laser. In contrast, for a superluminal laser, corresponding to a negative dispersion with a group index that is close to zero, its frequency shifts in the direction opposite to that of the Raman pump lasers, and has an amplitude that is larger by a factor approximately equaling the inverse of the group index. These findings would play a critical role in determining the maximum achievable sensitivity of sensors employing such lasers, especially under conditions where the pump laser linewidth is broadened significantly beyond the Schawlow-Townes linewidth due to classical fluctuations., Comment: 28 pages, 8 figures

Space situational awareness demands efficient monitoring of terrestrial sites and celestial bodies, necessitating advanced target recognition systems. Current target recognition systems exhibit limited operational speed due to challenges in handling substantial image data. While machine learning has improved this scenario, highresolution images remain a concern. Optical correlators, relying on analog processes, provide a potential alternative but are hindered by material limitations. Recent advancements in hybrid opto-electronic correlators (HOC) have addressed such limitations, additionally achieving shift, scale, and rotation invariant (SSRI) target recognition through use of the polar Mellin transform (PMT). However, there are currently no techniques for obtaining the PMT at speeds fast enough to take advantage of the inherent speed of the HOC. To that end, we demonstrate an optoelectronic PMT pre-processor that can operate at record-breaking millisecond frame rates using commercially available components for use in an automated SSRI HOC image recognition system for space situational awareness., Comment: Conference

The hybrid opto-electronic correlator (HOC) architecture has been shown to be able to detect matches in a shift, scale, and rotation invariant (SSRI) manner by incorporating a polar Mellin transform (PMT) pre-processing step. Here we demonstrate the design and use of a thick holographic memory disc (HMD) for high-speed SSRI correlation employing an HOC. The HMD was written to have 1,320 stored images, including both unprocessed images and their PMTs. We further propose and demonstrate a novel approach whereby the HOC inputs are spatially shifted to produce correlation signals without requiring stabilization of optical phases, yielding results that are in good agreement with the theory. Use of this approach vastly simplifies the design and operation of the HOC, while improving its stability significantly. Finally, a real-time opto-electronic PMT pre-processor utilizing an FPGA is proposed and prototyped, allowing for the automatic conversion of images into their PMTs without additional processing delay., Comment: Conference

We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schr\"odinger cat. In addition, this technique would make it possible to generate a mesoscopic Schr\"odinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.

We theoretically investigate the feasibility of applying spin squeezing to a light pulse atom interferometer in the presence of large momentum transfer using off-resonant Raman transitions, in order to enhance the sensitivity of accelerometry close to the Heisenberg limit. We also show how to implement this scheme in a dual-species atom interferometer for precision test of the equivalence principle by measuring the Eotvos parameter, and identify the spin squeezing protocol that is best suited for such an experiment. For a space borne platform in low earth orbit, such a scheme may eventually enable the measurement of the Eotvos parameter with a sensitivity of the order of 10^(-20).

Pump-probe microscopy of melanin in tumors has been proposed to improve diagnosis of malignant melanoma, based on the hypothesis that aggressive cancers disaggregate melanin structure. However, measured signals of melanin are complex superpositions of multiple nonlinear processes, which makes interpretation challenging. Polarization control during measurement and data fitting is used to decompose signals of melanin into their underlying molecular mechanisms. We then identify the molecular mechanisms that are most susceptible to melanin disaggregation and derive false-coloring schemes to highlight these processes in biological tissue. We exemplary demonstrate that false-colored images of a small set of melanoma tumors correlate with clinical concern. More generally, our systematic approach of decomposing pump-probe signals can be applied to a multitude of different samples., Comment: 12 pages, 4 figures

We present a generalized echo squeezing protocol (GESP) as a generalization of the Schr\"odinger cat state protocol (SCSP) with the value of the squeezing parameter being an arbitrary number rather than pi/2. We show analytically that over a broad range of the squeezing parameter the sensitivity reaches the Heisenberg limit (HL) within a factor of root-2. For a large number of particles, N, this plateau interval is almost the whole range from zero to pi/2, and the sensitivity is independent of the parity of N. Therefore, it is possible to operate a sensor over a wide interval of the squeezing parameter without changing the sensitivity. This is to be contrasted with the conventional echo squeezing protocol (CESP) which only works for a very small interval. In contrast to the CESP, the sensitivity of the GESP is close to the quantum Cram\'er-Rao bound over the whole range of the squeezing parameter. The enhancement in sensitivity for the GESP is due to a combination of two parameters: the phase magnification factor (PMF) and the noise amplification factor (NAF). As the value of the squeezing parameter increases, both PMF and NAF increase, keeping the ratio of PMF/NAF constant, yielding an enhancement of sensitivity at the HL within a factor of root-2. Thus, the robustness of the GESP against excess noise easily exceeds that of the CESP for a broad range of values of the squeezing parameter. As such, in the context of an experimental study, it should be possible to achieve a net enhancement in sensitivity higher than that for the CESP, under typical conditions where the excess noise exceeds the unsqueezed quantum projection noise. Finally, we consider the fragility of the GESP against collisions with background particles, and show how a balance between the fragility and the robustness against excess noise would in practice determine the optimal choice of parameters for the GESP.

A point source atom interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. Unlike a conventional light pulse atom interferometer, the PSI can produce a signal that corresponds to multi-axis rotation only, independent of acceleration. In addition, it can be used to measure acceleration along one direction, independent of rotation. Here, we describe a modified PSI that can be used to measure multi-axis rotation and multi-axis acceleration. Specifically, this type of PSI can be used to measure two-axes rotation around the directions perpendicular to the light pulses, as well as the acceleration in all three directions, with only one pair of Raman beams. Using two pairs of Raman beams in orthogonal directions sequentially, such a scheme would enable the realization of a complete atom interferometric inertial measurement unit.

The coherent population trapping (CPT) effect is used for making compact atomic clocks. There are two types of CPT clocks: the one in which the Raman beams are applied continuously and the one in which two CPT pulses separated by a dark period are applied (Ramsey scheme). It is obvious that the technique of spin squeezing can only be applied to the Ramsey CPT clock to enhance the sensitivity. However, it is not apparent how to adapt to the CPT clock the protocols for the microwave clock using one-axis-twist squeezing (OATS), since the Ramsey CPT clock is not trivially equivalent to the Ramsey microwave clock. In this paper, we show explicitly how to adapt two protocols using OATS, namely the Schr\"odinger cat state protocol (SCSP) and the generalization thereof, and the echo squeezing protocol (ESP), to the CPT clock. The ESP magnifies the phase shift by a factor of the square-root of (N/e), while the SCSP magnifies the phase shift by a factor of N/2 , making it able to achieve a higher sensitivity in the presence of excess noise., Comment: 32 pages, 5 figures

A point source interferometer (PSI) is a device where atoms are split and recombined by applying a temporal sequence of Raman pulses during the expansion of a cloud of cold atoms behaving approximately as a point source. The PSI can work as a sensitive multi-axes gyroscope that can automatically filter out the signal from accelerations. The phase shift arising from rotations is proportional to the momentum transferred to each atom from the Raman pulses. Therefore, by increasing the momentum transfer, it should be possibly to enhance the sensitivity of the PSI. Here, we investigate the degree of enhancement in sensitivity that could be achieved by augmenting the PSI with large momentum transfer (LMT) employing a sequence of many Raman pulses with alternating directions. Contrary to typical approaches used for describing a PSI, we employ a model under which the motion of the center of mass of each atom is described quantum mechanically. We show how increasing Doppler shifts lead to imperfections, thereby limiting the visibility of the signal fringes, and identify ways to suppress this effect by increasing the effective, two-photon Rabi frequencies of the Raman pulses. Taking into account the effect of spontaneous emission, we show that, for a given value of the one-photon Rabi frequency, there is an optimum value for the number of pulses employed, beyond which the net enhancement in sensitivity begins to decrease. For a one-photon Rabi frequency of 200 MHz, for example, the peak value of the factor of enhancement in sensitivity is ~39, for a momentum transfer that is ~69 times as large as that for a conventional PSI. We also find that this peak value scales as the one-photon Rabi frequency to the power of 4/5.

Experiments near the lock-in region in maximally dissipative non-Hermitian systems, e.g., conventional laser gyroscopes near the deadband, have run up against the Petermann limit, where excess noise exactly cancels any scale-factor enhancement resulting in no overall enhancement in precision. As a result, one might be tempted to conclude that exceptional points (EPs) generally cannot be used to increase the precision of laser sensors. Indeed, using a linear eigenmode analysis we show that the Petermann limit applies not just to maximally dissipative systems, but for any type of EP, owing to the fact that EPs are rotationally invariant. It turns out, however, that this restriction comes from the assumption of linearity. We find that nonlinearity breaks the rotation symmetry such that the different types of EPs are no longer equivalent above threshold. In particular, for sufficiently high measurement frequencies, EPs in conservatively coupled systems having a saturation imbalance can lead to an increase in the fundamental precision beyond the Petermann limit. Importantly, we find that only one mode lases under these conditions. We show that the beat note can be recovered by interference with an auxiliary mode, but that this has consequences for the quantum and classical noise that depend on the recovery scheme. Thus, it remains to be seen whether practical experiments can be designed that can take advantage of this enhancement.

We present two novel approaches to alter a flight network for introducing new flights while maximizing airline's profit. A key feature of the first approach is to adjust the aircraft cruise speed to compensate for the block times of the new flights, trading off flying time and fuel burn. In the second approach, we introduce aircraft swapping as an additional mechanism to provide greater flexibility in reducing the incremental fuel cost and adjusting the capacity. The nonlinear fuel-burn function and the binary aircraft swap and assignment decisions complicate the optimization problem significantly. We propose strong mixed-integer conic quadratic formulations to overcome the computational difficulties. The reformulations enable solving instances with 300 flights from a major U.S. airline optimally within reasonable compute times.

In a conventional atomic interferometer employing $N$ atoms, the phase sensitivity is at the standard quantum limit: $1/\sqrt{N}$. Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of $1/N$, while increasing the quantum noise by $\sqrt{N}$, thereby suppressing by the same factor the effect of excess noise. The protocol uses a Schr\"odinger Cat state representing a superposition of two collective states of $N$ atoms, behaving as a single entity with an $N$-fold increase in Compton frequency. The resulting $N$-fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schr\"odinger Cat state, with an $N$-fold increase in the effective transition frequency. We discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed. We find that the maximum improvement in sensitivity can be close to the ideal limit, for as many as ten million atoms., Comment: Single document, 12 figures

We present a protocol for an atomic interferometer that reaches the Heisenberg Limit (HL), within a factor of $\sim$ $\sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schr\"odinger cat (SC) state, as a superposition of two extremal collective states. When this SC interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of $Nm$, where $N$ is the number of particles in the ensemble, and $m$ is the mass of each particle. For $^{87}$Rb atoms, with $N=10^{6}$, for example, the intereference would occur at a Compton frequency of $\sim$ $2 \times 10^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of $N$. We present two variants of the protocol. Under Protocol A, the fringes are narrowed by a factor of $N$ for one parity, while for the other parity the signal is zero. Under Protocol B, the fringes are narrowed by a factor of $N$ for one parity, and by a factor of $\sqrt{N}$ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\sim$ $\sqrt{2}$ for both versions of the protocol. We show that when the SC interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of $N$, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of $N$, with a sensitivity that is equivalent to the HL, within a factor of $\sim$ $\sqrt{2}$., Comment: 7 figures