Pancharatnam Phase Research Articles

Resonance of vector vortex beams in a triangular optical cavity

We experimentally demonstrate resonance of first-order vector vortex beams (VVB) with a triangular optical cavity. We also show that, due to their symmetry properties, the VVBs commonly known as radial and azimuthal beams do not resonate at the same cavity length, which could be explored to use the triangular resonator as a mode sorter. In addition, an intracavity Pancharatnam phase shifter (PPS) is implemented in order to compensate for any birefringent phase that the cavity mirrors may introduce.

Experimental determination of Poincaré beam coordinates on a Hybrid order Poincaré sphere

Hybrid order Poincaré sphere (HyOPS) is used to represent Poincaré beams as points on it. The latitude and longitude of the HyOPS represent the size of the Stokes vortex ring and Pancharatnam phase of the Poincaré beam respectively. Although the HyOPS was introduced in 2015, there is no method that allows one to unambiguously determine the coordinates of Poincaré beams on this sphere. In this article, by subjecting the Poincaré beams to angular momentum and polarization transformations using conventional phase and polarizing elements respectively, we demonstrate an experimental method to determine the coordinates of the Poincaré beams on the HyOPS. This method may enable one to study the chirality and circular dichroism in materials and to enable us to segregate them, where both phenomena occur simultaneously.

Depiction of an external classical field effects on a four-level W-configuration atom embedded in a coherent cavity field

This paper examines the dynamics of a W-configuration four-level atom in a quantized cavity field and the system driven by an external classical field. By applying some canonical transformations, we derive analytical solutions to the Schrödinger equation for the corresponding Hamiltonian. We have analyzed the impact of the external field and detuning parameters on the system’s relative entropy of coherence, Wigner function, and Pancharatnam phase. Our findings suggest that the external field parameter greatly affects the coherence of the system, whereas the detuning parameters may increase its maximum bounds. Furthermore, we have utilized the Wigner function as a tool to measure the quantumness and classicality of the system in its phase space. Our results indicate that the external field has a greater impact on the classicality of the system than the detuning parameters. Additionally, we have observed rapid oscillations in the dynamics of the Pancharatnam phase for large detuning values. It is worth noting that the external field reduces the number of phase jumps in the system.

Invariants in copolar interferometry: An Abelian gauge theory

An $N$-element interferometer measures correlations among pairs of array elements. Closure invariants associated with closed loops among array elements are immune to multiplicative, element-based ("local") corruptions that occur in these measurements. Till recently, it has been unclear how a complete set of independent invariants can be analytically determined. We view the local, element-based corruptions in co-polar correlations as gauge tranformations belonging to the gauge group $\textrm{GL}(1,\mathbb{C})$. Closure quantities are then naturally gauge invariant. We use this to provide a simple and effective formalism, and identify the complete set of independent closure invariants from co-polar interferometric correlations using only quantities defined on $(N-1)(N-2)/2$ elementary and independent triangular loops. The $(N-1)(N-2)/2$ closure phases and $N(N-3)/2$ closure amplitudes (totaling $N^2-3N+1$ real invariants), familiar in astronomical interferometry, naturally emerge from this formalism, which unifies what has required separate treatments until now. We do not require auto-correlations, but can easily include them if reliably measured. This unified view clarifies issues relating to noise and inference of object model parameters. It also allows us to extend the rule of parallel transport associated with Pancharatnam phase in optics to apply to amplitudes as well. The framework presented here extends to $\textrm{GL}(2,\mathbb{C}$) for full polarimetric interferometry as presented in a companion paper, which generalizes and clarifies earlier work. Our findings are relevant to state of the art co-polar and full polarimetric very long baseline interferometry measurements to determine features very near the event horizons of blackholes at the centers of M87, Centaurus~A, and the Milky Way.

Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals

We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an AC electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied side-jump and skew-scattering processes, quantum interference diffractive contributions are now explicitly incorporated within the developed framework. This theory is applied to multifold fermions in topological semimetals, for which the generic formula for the skew scattering rate from the Pancharatnam phase is obtained along with the corresponding anomalous Hall conductivity.

Pancharatnam metals with integer and fractional quantum Hall effects

ABSTRACT Weakly interacting Fermi liquid can exhibit integer or fractional quantum Hall effect at sufficiently low temperatures, and in the presence of variable applied magnetic and/or electric fields. The said effects have been captured only incompletely by means of the Klitzing conductance formula, multiplied by the dimensionless filling factor (integer or fractional), ν because scattering rate cannot be absent for any conductor that is neither a perfect conductor at zero Kelvin (in the absence of phonons, scattering rate, Cooper pairing and Meissner effect) nor a superconductor. Here, we shall derive the proper microscopic resistance formula based on the notion of Pancharatnam phase retardation that captures both integer and fractional quantum Hall effects. We then compute the Planck constant from the Pancharatnam resistance formula, as well as provide a formal proof for this new formula. We shall unambiguously elaborate why the Pancharatnam resistance formula gives the complete physics of electron transport phenomena responsible for the quantum Hall effects, which include the changes to longitudinal and Hall resistance, as well as the temperature effect.

Properties of Pancharatnam Phase and Entanglement of a Five-Level Atom Interacting with a Squeezed Field

We introduce a quantum scheme where a single five-level atom interacts with a single-mode cavity field by a time-dependent coupling. During the interaction, the temporal behavior of the quantum entropy in the atomic basis is compared with that of the Mandel parameter used to quantify the nonclassical properties of the field. With the field prepared in a squeezed coherent state, the atomic quantum entropy is then used to quantify the entanglement or the nonlocal correlation of the five-level atom (5 LA) – field system. The influence of one- and two-photon transitions and the atomic motion on the degree of entanglement and the Pancharatnam phase is analyzed. The analysis emphasizes that both the time dependence and photon multiplicity play an important role in the evolution of the degree of entanglement, the Pancharatnam phase, and nonclassical properties. This insight may be very useful in various applications in quantum physics and quantum optics.

Pancharatnam Phase of Non-Hermitian Hamiltonian

Pancharatnam Phase of Non-Hermitian Hamiltonian

High-efficiency, tunable, fringe-field switching-mode beam steering based on a liquid crystal Pancharatnam phase

We have fabricated, characterized, and analyzed a recently proposed non-mechanical beam steering device based on the Pancharatnam-Berry phase in a liquid crystal. The architecture of our proposed device employs a linear array of phase control elements (PCEs) to locally control the orientation of the liquid crystal director into a cycloidal pattern to deflect transmitted light. The PCEs are comprised of a fringe-field switching electrode structure that can provide a variable in-plane electric field. Detailed optimization of the director configuration is in a good agreement with experimental results showing that the half-wave retardation condition has been uniformly achieved across the aperture. Moreover, efficiency simulations using a finite-difference time-domain algorithm verify a high beam steering efficiency for the proposed device.

Entanglement Control of Two-Level Atoms in Dissipative Cavities

An open quantum bipartite system consisting of two independent two-level atoms interacting nonlinearly with a two-mode electromagnetic cavity field is investigated by proposing a suitable non-Hermitian generalization of the Hamiltonian. The mathematical procedure of obtaining the corresponding wave function of the system is clearly given. Pancharatnam phase is studied to give a precise information about the required initial system state, which is related to artificial phase jumps, to control the degree of entanglement (DEM) and get the highest concurrence. We discuss the effect of time-variation coupling, and dissipation of both atoms and cavity. The effect of the time-variation function appears as frequency modulation (FM) effect in the radio waves. Concurrence rapidly reaches the disentangled state (death of entanglement) by increasing the effect of field decay. On the contrary, the atomic decay has no effect.

Design of a large aperture, tunable, Pancharatnam phase beam steering device.

Replacing mechanical optical beam steering devices with non-mechanical electro-optic devices has been a long-standing desire for applications such as space-based communication, LiDAR and autonomous vehicles. While promising progress has been achieved to non-mechanically deflect light with high efficiency over a wide angular range, significant limitations remain towards achieving large aperture beam steering with a tunable steering direction. In this paper, we propose a unique liquid crystal based Pancharatnam Phase Device for beam steering which can provide both tunability and a fast response times in a format scalable to large apertures. This architecture employs a linear array of phase control elements to locally control the orientation of the liquid crystal director into a cycloidal pattern to deflect transmitted light. The PCEs are comprised of a fringe field switching electrode structure that can provide a variable in-plane electric field. Detailed modeling of the proposed design is presented which demonstrates that such a device can achieve a high degree of uniformity as it rotates the LC molecules over the 180 ° angular range required to create a Pancharatnam phase device.

Time-dependent Pancharatnam phases and quantum correlations for coupling superconducting two-qubit system with dissipative environment

Two coupling superconducting qubits are studied for the quantum concurrence, discord, and Pancharatnam phase, for the X and Y states under the dephasing and instantaneous decay environment as well as their couplings. We find that the X and Y states are special mixed states according to the Bloch radius. In general, the larger the environment and phonon number are at the larger region of time, the larger the quantum concurrence and discord are. But we find that the environment correlations are helpful to implement the quantum computation. The Pancharatnam phases provide a way to distinguish the X and Y states.

A new method for detecting the nonlinearity of the Pancharatnam phase of light

A method based on the tracking of the peaks of interference fringes as a function of time-dependent analyzer setting is used to detect the Pancharatnam phase of light. The advantage of this method is demonstrated by observations of the nonlinearity of the Pancharatnam phase for certain paths on Poincare sphere where the fringe visibility reduces to almost zero. We also describe variations of this experiment with structured light beams, where the Pancharatnam phase leads to linear or nonlinear rotation of flower-pattern or spiral-shape interference fringes.

45‐2: Limits of Pancharatnam Phase lens for 3D/VR/AR Applications

Lenses based on Pancharatnam phase have recently attracted an increasing interest. Their main advantages include being very thin and inexpensive. But their application is generally limited to when a monochromatic illumination is used because they are strongly wavelength dependent. However low power Pancharatnam phase lenses have the potential to be considered for applications over the visible range. In this paper we provide intuitive “limits” for the power of these lenses under which these types of devices can be considered for use with applications with visible light that include human eye specifically for VR/AR applications.

Pancharatnam Phase of Two Two-Level Atoms Interacting with a Time-Dependent Cavity Field

Pancharatnam Phase of Two Two-Level Atoms Interacting with a Time-Dependent Cavity Field

Pancharatnam's phase advance and its validity for both integral and half-integral spins

If a time-dependent Hamiltonian is allowed to evolve adiabatically, and if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, we prove that the standard definition for the pure geometric phase is not pure after all and it is composed of both dynamic and geometric phases if the wavefunction is a proper wavefunction. Only with improper wavefunctions, the geometric phase can be shown to be a pure geometric phase. Therefore, any change to this so-called generalized geometric phase implies some interaction-induced changes to both the phase and group momenta of a proper wavefunction. Apart from that, the Pancharatnam phase advance, δ=π−12Ω is also proved to be valid for both integral and half-integral spins to the extent that the original Berry's phase formula is also proved to be a false representation of the geometric phase where Ω is the angle subtended on a sphere.

LC lens systems to solve accommodation/convergence conflict in three-dimensional and virtual reality displays

Accommodation–convergence mismatch is still an unsolved issue within the field of augmented reality, virtual reality, and three-dimensional systems in general. Solutions suggested to correct the focus cue in recent years require additional bandwidth, or compromise the image resolution. Our simple approach to overcome this issue is by using an eye-tracking system and electronic lenses. We propose an electronic hybrid lens system composed of segmented phase profile liquid crystal and Pancharatnam phase lenses. For practical application, eye tracking is necessary for measuring the toe-in of the user’s pupil to calculate the object depth. This information is used to determine the required diopteric power of the hybrid system. The optical performance and imaging quality of the proposed hybrid system are evaluated.

Multielectron geometric phase in intensity interferometry

Pancharatnam phase was discovered in the context of polarization optics in nineteen fifties. However, its full realization in quantum many-body systems still eludes us. This is primarily due to the fact that electron spin is not easily tunable. In the present proposal, we suggest that edge states of quantum spin Hall effect (QSHE) in conjunction with spin polarized electrodes (SPE) provide us with a unique opportunity to explore the Pancharatnam phase. We demonstrate the possibility of generating and detecting the multi-electron version of this phase that can as well be interpreted as multi-particle Aharonov-Bohm (A-B) effect in spin space arising solely due to spin dynamics. We further show that our proposed set-up leads to a robust interference pattern which survives orbital dephasing.

The post-selection operator current

In this paper, we develop the concept of the post-selection operator current and we use it to extend the methodology of quantum mechanics into related fields of science and engineering. We begin by reviewing some results from standard quantum mechanics. We then introduce the post-selection operator current and note that the concept of the operator current provides a common framework for connecting underlying concepts in classical signal theory and quantum mechanics. Next, we explore the geometry of post-selection making use of the Pancharatnam phase. We illustrate the usefulness of the method through a series of simple examples; at each stage we link the results of quantum mechanics to applications in signal processing. We then simplify some results by introducing a density operator. This simplification allows us to present a number of useful observations about weak values. We conclude by using the operator current explore the relationship between post-selection and gauge invariance. The methods developed in this paper enable us to characterize the time evolution of a post-selected operator. The methods can be applied to other evolutionary/transport equations including the Fokker–Planck equation, and the equation of Brownian motion.

"Achromatic limits" of Pancharatnam phase lenses.

Lenses based on the Pancharatnam phase have the advantage of being thin and inexpensive. Unfortunately, their optical effect is strongly wavelength dependent, and their applications generally are limited by the requirement of a monochromatic source. However, low-power lenses based on the Pancharatnam phase can be considered for applications over the visible range. In this paper, we provide intuitive "limits" for the lens power, below which these devices can be considered for use with the eye and visible light imaging applications.