Perturbative operator approach to high-precision light-pulse atom interferometry

Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like magnetic stray fields or blackbody radiation. Pushing the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here, we present a systematic operator expansion to obtain phase shifts and contrast analytically in powers of the perturbation. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects

Clock Transitions Versus Bragg Diffraction in Atom-interferometric Dark-matter Detection

Atom interferometers with long baselines are envisioned to complement the ongoing search for dark matter. They rely on atomic manipulation based on internal (clock) transitions or state-preserving atomic diffraction. Principally, dark matter can act on the internal as well as the external degrees of freedom to both of which atom interferometers are susceptible. We therefore study in this contribution the effects of dark matter on the internal atomic structure and the atoms' motion. In particular, we show that the atomic transition frequency depends on the mean coupling and the differential coupling of the involved states to dark matter, scaling with the unperturbed atomic transition frequency and the Compton frequency, respectively. The differential coupling is only of relevance when internal states change, which makes detectors, e.g., based on single-photon transitions sensitive to both coupling parameters. For sensors generated by state-preserving diffraction mechanisms like Bragg diffraction, the mean coupling modifies only the motion of the atom as the dominant contribution. Finally, we compare both effects observed in terrestrial dark-matter detectors

Multiphoton processes and higher resonances in the quantum regime of the free-electron laser

Despite exhibiting novel radiation features, the operation of the proposed quantum free-electron laser would have the drawback that the number of emitted photons is limited by one per electron, significantly reducing the output power of such a device. We show that relying on different resonances of the initial momentum of the electrons increases the number of emitted photons, but also increases the required length of the undulator impeding an experimetal realization. Moreover, we investigate how multiphoton processes influence the dynamics in the deep quantum regime

Controlling induced coherence for quantum imaging

Induced coherence in parametric down-conversion between two coherently pumped nonlinear crystals that share a common idler mode can be used as an imaging technique. Based on the interference between the two signal modes of the crystals, an image can be reconstructed. By obtaining an expression for the interference pattern that is valid in both the low- and the high-gain regimes of parametric down-conversion, we show how the coherence of the light emitted by the two crystals can be controlled. With our comprehensive analysis we provide deeper insight into recent discussions about the application of induced coherence to imaging in different regimes. Moreover, we propose a scheme for optimizing the visibility of the interference pattern so that it directly corresponds to the degree of coherence of the light generated in the two crystals. We find that this scheme leads in the high-gain regime to a visibility arbitrarily close to unity.Comment: 9 pages, 4 figure

Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography

High-dimensional encoding schemes have emerged as a novel way to perform quantum information tasks. For high dimensionality, temporal and transverse spatial modes of photons are the two paradigmatic degrees of freedom commonly used in such experiments. Nevertheless, general devices for multi-outcome measurements are still needed to take full advantage of the high-dimensional nature of encoding schemes. We propose a general full-field mode sorting scheme consisting only of up to two optimized phase elements based on evolutionary algorithms that allows for joint sorting of azimuthal and radial modes in a wide range of bases. We further study the performance of our scheme through simulations in the context of high-dimensional quantum cryptography, where high-fidelity measurement schemes are crucial

Light shifts in atomic Bragg diffraction

Bragg diffraction of an atomic wave packet in a retroreflective geometry with two counterpropagating optical lattices exhibits a light shift induced phase. We show that the temporal shape of the light pulse determines the behavior of this phase shift: In contrast to Raman diffraction, Bragg diffraction with Gaussian pulses leads to a significant suppression of the intrinsic phase shift due to a scaling with the third power of the inverse Doppler frequency. However, for box-shaped laser pulses, the corresponding shift is twice as large as for Raman diffraction. Our results are based on approximate, but analytical expressions as well as a numerical integration of the corresponding Schr\"odinger equation.Comment: 6 pages, 5 figure

A high-gain Quantum free-electron laser: emergence & exponential gain

We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum FEL in the high-gain mode and avoids the experimental challenges of an X-ray FEL oscillator. Moreover, we study the intensity fluctuations of the emitted radiation which turn out to be super-Poissonian

Optimal baseline exploitation in vertical dark-matter detectors based on atom interferometry

Several terrestrial detectors for gravitational waves and dark matter based on long-baseline atom interferometry are currently in the final planning stages or already under construction. These upcoming vertical sensors are inherently subject to gravity and thus feature gradiometer or multi-gradiometer configurations using single-photon transitions for large momentum transfer. While there has been significant progress on optimizing these experiments against detrimental noise sources and for deployment at their projected sites, finding optimal configurations that make the best use of the available resources are still an open issue. Even more, the fundamental limit of the device's sensitivity is still missing. Here we fill this gap and show that (a) resonant-mode detectors based on multi-diamond fountain gradiometers achieve the optimal, shot-noise limited, sensitivity if their height constitutes 20% of the available baseline; (b) this limit is independent of the dark-matter oscillation frequency; and (c) doubling the baseline decreases the ultimate measurement uncertainty by approximately 65%.Comment: 8 pages, 2 figure

Atomic diffraction from single-photon transitions in gravity and Standard-Model extensions

Single-photon transitions are one of the key technologies for designing and operating very-long-baseline atom interferometers tailored for terrestrial gravitational-wave and dark-matter detection. Since such setups aim at the detection of relativistic and beyond-Standard-Model physics, the analysis of interferometric phases as well as of atomic diffraction must be performed to this precision and including these effects. In contrast, most treatments focused on idealized diffraction so far. Here, we study single-photon transitions, both magnetically-induced and direct ones, in gravity and Standard-Model extensions modeling dark matter as well as Einstein-equivalence-principle violations. We take into account relativistic effects like the coupling of internal to center-of-mass degrees of freedom, induced by the mass defect, as well as the gravitational redshift of the diffracting light pulse. To this end, we also include chirping of the light pulse required by terrestrial setups, as well as its associated modified momentum transfer for single-photon transitions.Comment: 11 pages, 3 figures, 2 tables; This preprint has been submitted to AVS Quantum Scienc