Momentum States Research Articles

Statistical properties of the momentum occupation numbers of the Tonks-Girardeau gas in a harmonic trap

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero and finite temperature in a harmonic trap. We show that correlations between opposite momentum states $p$, which is an important fingerprint of long range order in weakly interacting Bose systems are suppressed. Non trivial correlations, including negative correlations are observed for momenta smaller or of the order of the inverse radius of the gas. The full distribution of the number of bosons with momentum $p$ exhibits an interesting crossover from a non trivial distribution at zero momentum to an exponential distribution. The distribution of the quasi-condensate occupation is also studied. Experimental relevance of our findings for recent cold atoms experiments are discussed.

Speckle in polarization structured light

We show that the far-field speckle patterns observed on the transmission of polarization structured light beams through a random diffuser screen have distinct spatial textures, which significantly differ from the texture of the fully developed scalar speckle. In particular, we report on speckle observed using the V-point and C-point polarization singular beams for illumination in this work. The V-point and C-point polarization singularities are generated by a combination of different orbital angular momentum (OAM) states in orthogonal polarizations. When passed through a random diffuser screen, the on-axis far-field diffraction intensity is an incoherent summation of speckle intensities due to the individual OAM states. Unlike the typical grainy structure in the scalar speckle, the speckle patterns observed with V-point and C-point illuminating beams are seen to have a noodle-like and sponge-like textures respectively. The speckle from V-point and C-point illuminations is difficult to distinguish using the usual intensity statistics which does not account for the distinct spatial structure of the speckle patterns. The Gray Level Co-occurrence Matrix (GLCM) methodology was therefore used to extract a number of spatial textural features from the speckle patterns observed using scalar and polarization structured illuminations. The principal component analysis (PCA) technique when applied to the texture parameters shows that it is possible to identify the nature of the illuminating beam by simply observing the texture properties of the resultant speckle pattern. When coherent light beams pass through a random medium resulting in a fully developed speckle pattern, the information regarding the profile of the input beam is generally considered to be lost. Our new observations on distinct textural features in speckle from structured light therefore suggest the possibility of information transmission through random media by means of switching the polarization structure of the incident beam.

Unscrambling OAM mode using digital phase-shifting in the Stokes fluctuations correlation

In this Letter, we propose and experimentally demonstrate a new, to the best of our knowledge, non-interferometric and highly stable technique to unscramble the incident orbital angular momentum (OAM) state and quantitatively measure the phase structure from the non-imaged random light. A new theoretical basis is developed and also verified by numerical simulation and experimental demonstration. We also quantitatively investigate the OAM modes of the incident light using orthogonal projection.

Stiffening of matter in quark-hadron continuity

We discuss stiffening of matter in quark-hadron continuity. We introduce a model that relates quark wave functions in a baryon and the occupation probability of states for baryons and quarks in dense matter. In a dilute regime, the confined quarks contribute to the energy density through the masses of baryons but do not directly contribute to the pressure; hence, the equations of state are very soft. This dilute regime continues until the low momentum states for quarks get saturated; this may happen even before baryons fully overlap, possibly at density slightly above the nuclear saturation density. After the saturation, the pressure grows rapidly while changes in energy density are modest, producing a peak in the speed of sound. If we use baryonic descriptions for quark distributions near the Fermi surface, we reach a description similar to the quarkyonic matter model of McLerran and Reddy. With a simple adjustment of quark interactions to get the nucleon mass, our model becomes consistent with the constraints from 1.4-solar mass neutron stars, but the high density part is too soft to account for two-solar mass neutron stars. We delineate the relation between the saturation effects and short range interactions of quarks, suggesting interactions that leave low density equations of state unchanged but stiffen the high density part.

Quantum State Control of a Bose-Einstein Condensate in an Optical Lattice

We report on the efficient design of quantum optimal control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our protocols operate on the momentum comb associated with the lattice. In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position. With this technique, we experimentally demonstrate a precise, robust and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components. This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

Effects of chiral MIT boundary conditions for a Dirac particle in a box

Abstract We investigate the effects of the chiral MIT boundary conditions for a Dirac particle in a 1D box. We show how the boundary condition affects the discrete momentum, energy level, transition frequency, and spin state in a box. The effects of the chiral MIT boundary conditions on the probability and scalar densities are also demonstrated. The results show that an asymmetric distribution appears in the box depending on the parameters of the spin orientation and chiral angle.

Contextuality-based quantum conferencing

Nonlocality inequalities for multi-party systems act as contextuality inequalities for single qudit systems of suitable dimensions (Heywood and Redhead in Found Phys 13(5):481–499, 1983; Abramsky and Brandenburger in New J Phys 13(11):113036, 2011). In this paper, we propose the procedure for adaptation of nonlocality-based quantum conferencing protocols (NQCPs) to contextuality-based QCPs (CQCPs). Unlike the NQCPs, the CQCPs do not involve nonlocal states. As an illustration of the procedure, we present a QCP based on Mermin’s contextuality inequality. As a significant improvement, we propose a QCP based on CHSH contextuality inequality involving only four-dimensional states irrespective of the number of parties sharing the key. The key generation rate of the latter is twice that of the former. Although CQCPs allow for an eavesdropping attack which has no analog in NQCPs, a way out of this attack is demonstrated. Finally, we examine the feasibility of experimental implementation of these protocols with orbital angular momentum states.

Nonlinear Dynamics in a Synthetic Momentum-State Lattice.

The scope of analog simulation in atomic, molecular, and optical systems has expanded greatly over the past decades. Recently, the idea of synthetic dimensions-in which transport occurs in a space spanned by internal or motional states coupled by field-driven transitions-has played a key role in this expansion. While approaches based on synthetic dimensions have led to rapid advances in single-particle Hamiltonian engineering, strong interaction effects have been conspicuously absent from most synthetic dimensions platforms. Here, in a lattice of coupled atomic momentum states, we show that atomic interactions result in large and qualitative changes to dynamics in the synthetic dimension. We explore how the interplay of nonlinear interactions and coherent tunneling enriches the dynamics of a one-band tight-binding model giving rise to macroscopic self-trapping and phase-driven Josephson dynamics with a nonsinusoidal current-phase relationship, which can be viewed as stemming from a nonlinear band structure arising from interactions.

Matter-wave interferometry with helium atoms in low- l Rydberg states

Electric Rydberg-atom interferometry has been performed with helium atoms in coherent superpositions of the $1s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $1s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ Rydberg levels. The experiments were carried out in a longitudinal geometry with the atoms traveling at 2000 m/s in pulsed supersonic beams. After laser photoexcitation from the $1s2s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ metastable level, coherent manipulation of the population of the Rydberg states was achieved using sequences of microwave pulses. The difference in the static electric dipole polarizabilities of the $1s56s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $1s57s\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ levels allowed superpositions of external momentum states to be generated when inhomogeneous electric fields were used to exerted forces on the atoms prepared in superpositions of these internal states. Interference fringes, with contributions arising from the spatial separation of these Rydberg-atom wave packets in the direction of propagation of the atomic beam, were identified through changes in the internal-state populations as the magnitudes and durations of the time-dependent electric-field gradient pulses were adjusted. The maximal displacement of the atomic wave packets for which interference fringes were observed was $\ensuremath{\sim}0.75\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$, limited by the longitudinal velocity spread in the atomic beam and the characteristics of the inhomogeneous electric-field distribution in the apparatus. The experimental data are in good quantitative agreement with the results of numerical calculations of the time evolution of the atomic states under the experimental conditions.

Photons, Orbital Angular Momentum, and Neutrons

In article number 2000257, Ronald L. Cappelletti and John Vinson consider intentionally restricting the transverse size of light used to create orbital angular momentum (OAM) states. Interference between a unit OAM state and a plane wave gives a distinctive fork dislocation pattern. However, this fork is also created by adding the patterns of individual waves of width W, each not having a unit of OAM, as shown on the cover. A phase contrast image is not in itself sufficient evidence of unit OAM. The same is true of matter waves. The implications for producing OAM in individual neutrons are considered.

Determination of Energy Spectra By Using Proper Quantization Rule of Woods-Saxon Potential

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) is calculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimized potential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of the nuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution of energy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlab calculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the result with the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four light nuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of these nuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearson correlation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, we plot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a good agreement between the results of this work and experimental values.

Representation of total angular momentum states of beams through a four-parameter notation

It has been confirmed beams carrying total angular momentums (TAMs) that consist of spin angular momentums (SAMs) and orbital angular momentums (OAMs) are widely used in classical and quantum optics. Here we propose and demonstrate a new kind of representation consisting of four real numbers to describe the TAM states of arbitrary beams. It is shown that any homogeneous polarization, scalar vortices and complex vectorial vortex field, all of which result from the TAMs of photons, can be well represented conveniently using our proposed four-parameter representation. Furthermore, the proposed representation can also reveal the internal change of TAMs as the conversion between SAMs and OAMs. The salient properties of the proposed representation is to give a universal form of TAMs associated with complicated polarizations and more exotic vectorial vortex beams, which offer an important basis for the future applications.

Multiple Longitudinal Polarization Vortices Generated via All‐Silicon Metasurface

AbstractPhotons carry spin angular momentum and orbital angular momentum, vortex beams with helical phase fronts provide a new understanding of optical and physical phenomena. Here, the creation of four longitudinal polarized vortices with arbitrary topological charges is demonstrated using all‐silicon metasurfaces in terahertz band, integrating propagation phase and Pancharatnam–Berry phase. This efficient scheme allows the authors to flexibly control the longitudinal polarized electric field by designing the field distribution of the transverse polarization. As a proof of concept, two metasurfaces are designed to demonstrate the flexibility of such approach. One is used to generate dual longitudinal polarized superpositions of orbital angular momentum states with arbitrary topological charges, and the other is designed to generate four discrete longitudinal vortices. This method may find applications in manipulation of electron bunches and new imaging technology.

Enhanced detection techniques of orbital angular momentum states in the classical and quantum regimes

The orbital angular momentum (OAM) of light has been at the center of several classical and quantum applications for imaging, information processing and communication. However, the complex structure inherent in OAM states makes their detection and classification nontrivial in many circumstances. Most of the current detection schemes are based on models of the OAM states built upon the use of Laguerre–Gauss (LG) modes. However, this may not in general be sufficient to capture full information on the generated states. In this paper, we go beyond the LG assumption, and employ hypergeometric-Gaussian (HyGG) modes as the basis states of a refined model that can be used—in certain scenarios—to better tailor OAM detection techniques. We show that enhanced performances in OAM detection are obtained for holographic projection via spatial light modulators in combination with single-mode fibers (SMFs), and for classification techniques based on a machine learning approach. Furthermore, a three-fold enhancement in the SMF coupling efficiency is obtained for the holographic technique, when using the HyGG model with respect to the LG one. This improvement provides a significant boost in the overall efficiency of OAM-encoded single-photon detection systems. Given that most of the experimental works using OAM states are effectively based on the generation of HyGG modes, our findings thus represent a relevant addition to experimental toolboxes for OAM-based protocols in quantum communication, cryptography and simulation.

Engineering transient hyperbolic metamaterials using InAsSb-based semiconductor

The authors demonstrate the ability to create an ultrafast hyperbolic momentum state using metallic InAsSb alloys embedded within dielectric GaSb and explore the possibility of transient modification of metamaterials to control the optical properties of photon emission. Properly engineered quantum well structures were grown by molecular beam epitaxy and Si-doped in order to convert the InAsSb layers from dielectric to metallic at infrared frequencies. The carrier excitation scheme of the engineered hyperbolic stacks was investigated in a variety of excitation levels using pump–probe measurements. The photo-excited carriers in the structure with a metal fraction of ∼0.5 showed a polarization dependent reflectivity change, which indicates a transient hyperbolic metamaterial state in the heterostructure induced by the pump laser.

Nonlinear Wavy Metasurfaces with Topological Defects for Manipulating Orbital Angular Momentum States

Nonlinear Wavy Metasurfaces with Topological Defects for Manipulating Orbital Angular Momentum States

Efficient Method for an Approximate Treatment of the Coriolis Effect in Calculations of Quantum Dynamics and Spectroscopy, with Application to Scattering Resonances in Ozone.

A numerical approach is developed to capture the effect of rotation-vibration coupling in a practically affordable way. In this approach only a limited number of adjacent rotational components are considered to be coupled, while the couplings to other rotational components are neglected. This partially coupled (PC) approach permits to reduce the size of Hamiltonian matrix significantly, which enables the calculations of ro-vibrational states above dissociation threshold (scattering resonances) for large values of total angular momentum. This method is employed here to reveal the role of the Coriolis effect in the ozone formation reaction at room temperature, dominated by large values of total angular momentum states, on the order of J = 24 and 28. We found that, overall, the effect of ro-vibrational coupling is not minor for large J. Compared to the results of symmetric top rotor approximation, where the ro-vibrational coupling is neglected, we found that the widths of scattering resonances, responsible for the lifetimes of metastable ozone states, remain nearly the same (on average), but the number of these states increases by as much as 20%. We also found that these changes are nearly the same in symmetric and asymmetric ozone isotopomers 16O18O16O and 16O16O18O. Therefore, based on the results of these calculations, the Coriolis coupling does not seem to favor the formation of asymmetric ozone molecules and thus cannot be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes.

Phase shift of double-diffraction Raman interference due to high-order diffraction states

Double-diffraction Raman interference is a novel interference scheme developed in recent years. It has a potentially high measurement precision due to the symmetric interference loop with identical internal states. In this paper, we analyze the high-order diffraction process in double-diffraction Raman interference and derive state evolution equations that include multiple diffraction processes. The population evolution of the states and the Mach-Zehnder interference fringe are calculated under the action of a Raman laser. The thermal momentum distribution averaging and state grouping methods are employed to solve the problem of decoherence at different interference exit ports. We compare the phase shifts calculated by integrating the sensitivity function and the two-photon frequency shift and by numerically solving the state evolution equations with high-order diffraction states. The good agreement between the results of the two methods shows that the two-photon frequency shift is the main reason for the phase shift induced by the higher-order diffraction states. Finally, the test error of an equivalent principle test experiment due to this effect is analyzed. This paper may be helpful for the analysis and suppression of the systemic error in such experiments.

Dissipation and energy gap

The effect of anharmonicity (coupling) in the field theory generally results in dissipation of plane waves. It has been appreciated that anharmonicity and ensuing dissipation of plane waves can be accompanied by the emergence of the gapped momentum state. Here, we show that the same effect can lead to a gapped energy state and a dispersion relation where the frequency (energy) gap emerges explicitly. We discuss several notable properties of gapped energy and momentum states and connections between them.

Alternative method of generating gamma rays with orbital angular momentum

We study an alternative method of generating gamma rays with orbital angular momentum (OAM). Accelerated partially-stripped ions are used as an energy up-converter. Irradiating an optical laser beam with OAM on ultrarelativistic ions, they are excited to a state of large angular momentum. Gamma rays with OAM are emitted in their deexcitation process. We examine the excitation cross-section and deexcitation rate.