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We investigate electrical transport in a quantum wire of $N$ sites connected to an equal number $(N_i/2)$ of sources and drains of charges in bulk. Each source and drain injects and extracts charges at the same rate, respectively. We show that the linear-response electrical current is nonreciprocal in such a system when the arrangement of sources and drains breaks the system's parity. We prove that inelastic scattering is essential for nonreciprocity in this system. For this, we invoke a master equation description of classical charge transport in a similar system. The nonreciprocal current in quantum wire matches that in the classical model for $N_i/N \sim 1$, generating a finite scattering length much smaller than the length of the wire. The nonreciprocity in the quantum wire oscillates with wire length when $N_i/N \ll 1$, and it can vanish at specific lengths.

We propose a method to directly probe bulk topological quantum numbers in topological matter by measuring the momentum-space single-particle spectral function (SPSF). Angle-resolved photoemission spectroscopy (ARPES) can detect SPSF and is often used to determine the bulk band structure of quantum materials. Here, we show that while one part of the momentum-space SPSF gives band structure, it also contains the knowledge of winding and Chern numbers of various topological materials. For this, we derive SPSF in three different models of topological systems, such as the Kitaev model of topological superconductors, the long-range Su-Schrieffer-Heeger model, and the Qi-Wu-Zhang model and explain how to extract the winding or Chern numbers in different topological phases from the SPSF. Such information from SPSF seems experimentally accessible due to the recent advancement of ARPES and scanning tunneling spectroscopy techniques., Comment: 13 pages, 9 figures

We show nonreciprocal light propagation for single-photon inputs due to quantum noise in coupled optical systems with gain and loss. We consider two parity-time ($\mathcal{PT}$) symmetric linear optical systems consisting of either two directly coupled resonators or two finite-length waveguides evanescently coupled in parallel. One resonator or waveguide is filled with an active gain medium and the other with a passive loss medium. The light propagation is reciprocal in such $\mathcal{PT}$ symmetric linear systems without quantum noise. We show here that light transmission becomes nonreciprocal when we include quantum noises in our modeling, which is essential for a proper physical description. The quantum nonreciprocity is especially pronounced in the $\mathcal{PT}$ broken phase. Transmitted light intensity in the waveguide of incidence is asymmetric for two waveguides even without noise. Quantum noise significantly enhances such asymmetry in the broken phase., Comment: 12 pages, 4 figures

We investigate heat transport through a one-dimensional open coupled scalar field theory, depicted as a network of harmonic oscillators connected to thermal baths at the boundaries. The non-Hermitian dynamical matrix of the network undergoes a stability-to-instability transition at the exceptional points as the coupling strength between the scalar fields increases. The open network in the unstable regime, marked by the emergence of inverted oscillator modes, does not acquire a steady state, and the heat conduction is then unbounded for general bath couplings. In this work, we engineer a unique bath coupling where a single bath is connected to two fields at each edge with the same strength. This configuration leads to a finite steady-state heat conduction in the network, even in the unstable regime. We also study general bath couplings, e.g., connecting two fields to two separate baths at each boundary, which shows an exciting signature of approaching the unstable regime for massive fields. We derive analytical expressions for high-temperature classical heat current through the network for different bath couplings at the edges and compare them. Furthermore, we determine the temperature dependence of low-temperature quantum heat current in different cases. Our study will help to probe topological phases and phase transitions in various quadratic Hermitian bosonic models whose dynamical matrices resemble non-Hermitian Hamiltonians, hosting exciting topological phases., Comment: 19 pages, 4 figures

Composite topological phases with intriguing topology like M${\"o}$bius strips emerge in sublattice symmetric non-Hermitian systems due to spontaneous breaking of time-reversal symmetry at some parameter regime. While these phases have been characterized by nonadiabatic complex geometric phases of multiple participating complex bands, the physical properties of these phases largely remain unknown. We explore the dynamical response of these phases by studying Loschmidt echo from an initial state of the Hermitian Su-Schrieffer-Heeger (SSH) model, which is evolved by a non-Hermitian SSH Hamiltonian after a sudden quench in parameters. Topology-changing quenches display non-analytical temporal behavior of return rates (logarithm of the Loschmidt echo) for the non-Hermitian SSH Hamiltonian in the trivial, M${\"o}$bius and topological phase. Moreover, the dynamical topological order parameter appears only at one side of the Brillouin zone for the M${\"o}$bius phase case in contrast to both sides of the Brillouin zone for quench by the trivial and topological phase of the non-Hermitian SSH model. The last feature is a dynamical signature of different symmetry constraints on the real and imaginary parts of the complex bands in the M${\"o}$bius phase., Comment: 10 pages, 6 figures

We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size $(L)$ scaling of Thouless time $t^*$, beyond which the spectral form factor follows the prediction of random matrix theory. The $L$-dependence of $t^*$ crosses over from $\log L$ to $L^2$ with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-sized chain, and it finally settles to $t^* \propto \mathcal{O}(L^2)$ in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to $t^*\propto \mathcal{O}(\log L)$, previously predicted for single species of qubits or fermions without total number conservation., Comment: 15 pages, 8 figures

We explore special features of quantum light-matter interactions inside structured waveguides due to their finite bandwidth, band edges, and non-trivial topological properties. We model the waveguides as either a tight-binding (TB) chain or a Su-Schrieffer-Heeger (SSH) chain. For unstructured waveguides with infinite bandwidth, the transmission and reflection amplitude of a side-coupled two-level emitter (2LE) are the same as the reflection and transmission amplitude of a direct-coupled 2LE. We show that this analogy breaks down for structured waveguides with finite bandwidth due to the appearance of Lamb shift only for the direct-coupled 2LE. We further predict a robust light-emitter coupling at zero collective decay width of a single giant 2LE (with two couplings at different points) near the band edges of the structured waveguides where topological features can be beneficial. Finally, we study single-photon dynamics in a heterojunction of a long TB and short SSH waveguide connected to a 2LE at the SSH end. We show the propagation of a photon from the excited emitter to the TB waveguide only when the SSH waveguide is in the topological phase. Thus, the heterojunction acts as a quantum switch or conditional propagation channel., Comment: 15 pages, 11 figures

In this paper, we introduce a semi-decentralized control technique for a swarm of robots transporting a fragile object to a destination in an uncertain occluded environment.The proposed approach has been split into two parts. The initial part (Phase 1) includes a centralized control strategy for creating a specific formation among the agents so that the object to be transported, can be positioned properly on the top of the system. We present a novel triangle packing scheme fused with a circular region-based shape control method for creating a rigid configuration among the robots. In the later part (Phase 2), the swarm system is required to convey the object to the destination in a decentralized way employing the region based shape control approach. The simulation result as well as the comparison study demonstrates the effectiveness of our proposed scheme., Comment: 7 pages,8 figures, IEEE International Conference on Robotics and Automation (ICRA) 2023

While the theoretical studies in waveguide quantum electrodynamics predominate with single-photon and two-photon Fock state (photon number states) input, the experiments are primarily carried out using a faint coherent light. We create a theoretical toolbox to compare and contrast linear and nonlinear light scattering by a two-level or a three-level emitter embedded in an open waveguide carrying Fock state or coherent state inputs. We identify rules to compare light transport properties, the Kerr, and cross-Kerr nonlinearities of the medium for the two types of inputs. A generalized description of the Kerr and cross-Kerr effect for different types of inputs is formulated to compare the Kerr and cross-Kerr nonlinearity between two photons in these models., Comment: 10 pages, 1 figure

We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pairing terms are absent, the effective Hamiltonian has a non-abelian $SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless time with the system size, irrespective of the particle number. This is a consequence of degenerate symmetry multiplets of the subleading eigenvalue of the effective Hamiltonian and is broken by the pairing terms. In the latter case, we numerically find a nontrivial systematic system-size dependence of the Thouless time, in contrast to a related recent study for kicked fermionic chains., Comment: 9 pages, 8 figures

The multipartite non-Hermitian Su-Schrieffer-Heeger model is explored as a prototypical example of one-dimensional systems with several sublattice sites for unveiling intriguing insulating and metallic phases with no Hermitian counterparts. These phases are characterized by composite cyclic loops of multiple complex-energy bands encircling single or multiple exceptional points (EPs) on the parametric space of real and imaginary energy. We show the topology of these composite loops is similar to well-known topological objects like M\"obius strips and Penrose triangles, and can be quantified by a nonadiabatic cyclic geometric phase which includes contributions only from the participating bands. We analytically derive a complete phase diagram with the phase boundaries of the model. We further examine the connection between the encircling of multiple EPs by complex-energy bands on parametric space and associated topology., Comment: non-Hermitian physics, topology, composite loops, Complex Zak phase, Composite Zak phase, topological invariant, M\"obius strips, Penrose triagle

We consider the motion of a light sail that is accelerated by a powerful laser beam. We derive the equations of motion for two proof-of-concept sail designs with damped internal degrees of freedom. Using linear stability analysis we show that perturbations of the sail movement in all lateral degrees of freedom can be damped passively. This analysis also shows complicated behaviour akin to that associated with exceptional points in PT-symmetric systems in optics and quantum mechanics. The excess heat that is produced by the damping mechanism is likely to be substantially smaller than the expected heating due to the partial absorption of the incident laser beam by the sail., Comment: 7 figures

We study the thermalization of a small $XX$ chain coupled to long, gapped $XXZ$ leads at either side by observing the relaxation dynamics of the whole system. Using extensive tensor network simulations, we show that such systems, although not integrable, appear to show either extremely slow thermalization or even lack thereof since the two can not be distinguished within the accuracy of our numerics. We show that the persistent oscillations observed in the spin current in the middle of the $XX$ chain are related to eigenstates of the entire system located within the gap of the boundary chains. We find from exact diagonalization that some of these states remain strictly localized within the $XX$ chain and do not hybridize with the rest of the system. The frequencies of the persistent oscillations determined by numerical simulations of dynamics match the energy differences between these states exactly. This has important implications for open systems, where the strongly interacting leads are often assumed to thermalize the central system. Our results suggest that if we employ gapped systems for the leads, this assumption does not hold; this finding is particularly relevant to any potential future experimental studies of open quantum systems., Comment: 6 pages, 4 figures

We report non-invasive detection of spin coherence in a collection of Raman-driven cold atoms using dispersive Faraday rotation fluctuation measurements, which opens up new possibilities of probing spin correlations in quantum gases and other similar systems. We demonstrate five orders of magnitude enhancement of the measured signal strength than the traditional spin noise spectroscopy with thermal atoms in equilibrium. Our observations are in good agreement with the comprehensive theoretical modeling of the driven atoms at various temperatures. The extracted spin relaxation rate of cold rubidium atoms with atom number density $\sim$10$^9/$cm$^3$ is of the order of 2$\pi\times$0.5 kHz at 150 $\mu$K, two orders of magnitude less than $\sim$ 2$\pi\times$50 kHz of a thermal atomic vapor with atom number density $\sim$10$^{12}/$cm$^3$ at 373 K., Comment: 11 pages, 11 figures

In this note we prove that almost cap sets $A \subset \mathbb{F}_q^n$, i.e., the subsets of $\mathbb{F}_q^n$ that do not contain too many arithmetic progressions of length three, satisfy that $|A| < c_q^n$ for some $c_q < q$. As a corollary we prove a multivariable analogue of Ellenberg-Gijswijt theorem., Comment: 5 pages

A non-Hermitian generalization of the Su-Schrieffer-Heeger model driven by a periodic external potential is investigated, and its topological features are explored. We find that the bi-orthonormal geometric phase acts as a topological index, well capturing the presence/absence of the zero modes. The model is observed to display trivial and non-trivial insulator phases and a topologically non-trivial M${\"o}$bius metallic phase. The driving field amplitude is shown to be a control parameter causing topological phase transitions in this model. While the system displays zero modes in the metallic phase apart from the non-trivial insulator phase, the metallic zero modes are not robust, as the ones found in the insulating phase. We further find that zero modes' energy converges slowly to zero as a function of the number of dimers in the M${\"o}$bius metallic phase compared to the non-trivial insulating phase., Comment: 13 pages, 8 figures

We investigate the role of optical nonlinearity in light propagation through two different one-dimensional open QED lattices, namely a chain of qubits with direct coupling between the nearest neighbors and a chain of connected resonators to each of which a qubit is side-coupled. Using the more accurate truncated Heisenberg-Langevin equations method we show a reduction of light transmission with increasing intensity in these lattices due to effective photon-photon interactions and related photon blockade mediated by nonlinearity in qubits. In contrast to the direct-coupled qubits, we find a revival in the light transmission in the side-coupled qubits at relatively higher intensities due to saturation of qubits by photons. We find that in absence of bulk dissipation the standard quasi-classical analysis fails to capture the reduction in light transmission due to effective photon-photon interaction. We then devise a systemic method to modify the quasi-classical analysis to give much better results., Comment: 19 pages, 11 figures

We study nonequilibrium transport in various open quantum systems whose systems and leads/baths are made of topological superconductors (TSs), semiconductors, and metals. Using quantum Langevin equations and Green's function method, we derive exact expressions for steady-state electrical, thermal, and spin current at the junctions between a system and leads. We validate these current expressions by comparing them with the results from direct time-evolution simulations. We then show how an electrical current injected in TS wires divides into two parts carried by single electronic excitations and Cooper pairs. We further show ballistic thermal transport in an open TS wire in the topological phase under temperature or voltage bias. The thermal current values grow significantly near the topological phase transition, where thermal conductance displays a sharp quantized peak as predicted earlier. We relate the quantized thermal conductance to the zero-frequency thermoelectric transmission coefficient of the open TS wire. We also observe a large thermoelectric current near the topological transition of the TS wires. We introduce a differential spin conductance which displays a quantized zero-bias peak at zero temperature for a spinful TS wire in the topological phase. The role of superconducting baths in transport is demonstrated by thoroughly examining the features of zero-temperature differential electrical conductance and thermal conductance in open systems with TS baths. Our new thermoelectric and spin transport findings in various two-terminal geometries are beneficial to the present challenges in probing the emergence of Majorana quasi-particles in experiments., Comment: 64 pages, 14 figures

The exact number of CNOT and single qubit gates needed to implement a Quantum Algorithm in a given architecture is one of the central problems of Quantum Computation. In this work we study the importance of concise realizations of Partially defined Unitary Transformations for better circuit construction using the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k \right>)$ are an important class of entangled states with uses in many branches of Quantum Information. In this regard we provide the most efficient Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit gate counts in comparison to existing literature. We further observe that our improvements also reduce architectural constraints of the circuits. We implement the circuit for preparing $\left| D^4_2 \right>$ on the "ibmqx2" machine of the IBM QX service and observe that the error induced due to noise in the system is lesser in comparison to the existing circuit descriptions. We conclude by describing the CNOT map of the generic $\left| D^n_k \right>$ preparation circuit and analyze different ways of distributing the CNOT gates in the circuit and its affect on the induced error., Comment: 13 pages, 22 figures

In this paper, we propose a novel non-contact vibration measurement system that is competent in estimating linear and/or rotational motions of machine parts. The technique combines microwave radar, standard camera, and optical strobe to capture vibrational or rotational motions in a relatively fast and affordable manner when compared to the current technologies. In particular, the proposed technique is capable of not only measuring common vibrational parameters (e.g. frequency, motor rpm, etc.) but also provides spatial information of the vibrational sources so that the origin of each vibrational point can be identified accurately. Furthermore, it can also capture the wobbling motion of the rotating shafts. Thus, the proposed method can find immense applications in preventive maintenance across various industries where heavy machinery needs to be monitored unobtrusively or there is a requirement for non-contact multi-point vibration measurement for any machine inspection applications.

We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains, and for timescales that exceed the so-called Thouless/Ehrenfest time which scales with the size $L$ as ${\cal O}(L^2)$, or ${\cal O}(L^0)$, in the presence, or absence of $U(1)$ symmetry, respectively. Using random phase assumption which essentially requires long-range nature of interaction, we demonstrate that the Thouless time scaling is equivalent to the behavior of the spectral gap of a classical Markov chain, which is in the continuous-time (Trotter) limit generated, respectively, by a gapless $XXX$, or gapped $XXZ$, spin-1/2 chain Hamiltonian., Comment: 6 pages, 1 figure

We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a V and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider $\Lambda$, V, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations approach to investigate the scattering of a probe and a drive beams both initially in a coherent state. We particularly calculate the regime of the probe and drive powers when the 3LE acts most efficiently as a coherent amplifier, and derive the second-order coherence of amplified probe photons. Finally, we apply the Kramers-Kronig relations to correlate the amplitude and phase response of the probe beam, which are used in finding the coherent amplification and the cross-Kerr phase shift in these systems., Comment: 17 pages, 10 figures, published version

Three decades ago, in a celebrated work, Zak found an expression for the geometric phase acquired by an electron in a one-dimensional periodic lattice as it traverses the Bloch band. Such a geometric phase is useful in characterizing the topological properties and the electric polarization of the periodic system. Unfortunately Zak's expression suffers from two flaws: its value depends upon the choice of origin of the unit cell, and is gauge dependent. Here we explain that these flaws in Zak's expression arise from the assumption that the electron's adiabatic motion is cyclic in the sense of recurrence of the density matrix in course of time evolution. We find through a careful investigation that the system displays cyclicity in a generalized sense wherein the physical observables return in the course of evolution. This notion of generalized cyclicity paves the way for a correct and consistent expression for the geometric phase in this system, christened as Pancharatnam-Zak phase. Pancharatnam-Zak geometric phase does not suffer from the flaws inherent in Zak's expression, and correctly classifies the Bloch bands of the lattice. A natural filled band extension of the Pancharatnam-Zak phase is also constructed and studied., Comment: 24 pages, 4 figures

We investigate the dynamics of hybrid junctions made of the topological superconductor (TS) and normal metal (N) wires. We consider an X-Y-Z configuration for the junctions where X, Y, Z = TS, N. We assume the wires X and Z being semi-infinite and in thermal equilibrium. We connect the wires X and Z through the short Y wire at some time, and numerically study time-evolution of the full device. For TS-N-TS device, we find a persistent, oscillating electrical current at both junctions even when there is no thermal or voltage bias, and the TS wires are identical. The amplitude and period of the oscillating current depend on the initial conditions of the middle N wire indicating the absence of thermalization. This zero-bias current vanishes at a long time for any of X and Z being an N wire or a TS wire near a topological phase transition. Using properties of different bound states within the superconducting gap, we develop a clear understanding of the oscillating currents., Comment: 10 pages, 6 figures