We present a tutorial on the properties of the new ideal circuit element, a memristor. By definition, a memristor M relates the charge q and the magnetic flux φ in a circuit, and complements a resistor R, a capacitor C, and an inductor L as an ingredient of ideal electrical circuits. The properties of these three elements and their circuits are a part of the standard curricula. The existence of the memristor as the fourth ideal circuit element was predicted in 1971 based on symmetry arguments, but was clearly experimentally demonstrated just this year. We present the properties of a single memristor, memristors in series and parallel, as well as ideal memristorcapacitor (MC), memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. We find that the memristor has hysteretic current-voltage characteristics. We show that the ideal MC (ML) circuit undergoes non-exponential charge (current) decay with two time-scales, and that by switching the polarity of the capacitor, an ideal MCL circuit can be tuned from overdamped to underdamped. We present simple models which show that these unusual properties are closely related to the memristor's internal dynamics. This tutorial complements the pedagogy of ideal circuit elements (R, C, and L) and the properties of their circuits.

Open physical systems with balanced loss and gain, described by non-Hermitian parity-time reflection symmetric Hamiltonians, exhibit a transition which could engender modes that exponentially decay or grow with time, and thus spontaneously breaks the -symmetry. Such -symmetry-breaking transitions have attracted many interests because of their extraordinary behaviors and functionalities absent in closed systems. Here we report on the observation of -symmetry-breaking transitions by engineering time-periodic dissipation and coupling, which are realized through state-dependent atom loss in an optical dipole trap of ultracold 6Li atoms. Comparing with a single transition appearing for static dissipation, the time-periodic counterpart undergoes -symmetry breaking and restoring transitions at vanishingly small dissipation strength in both single and multiphoton transition domains, revealing rich phase structures associated to a Floquet open system. The results enable ultracold atoms to be a versatile tool for studying -symmetric quantum systems.

Open systems with gain and loss, described by non-trace-preserving, non-Hermitian Hamiltonians, have been a subject of intense research recently. The effect of exceptional-point degeneracies on the dynamics of classical systems has been observed through remarkable phenomena such as the paritytime symmetry breaking transition, asymmetric mode switching, and optimal energy transfer. On the other hand, consequences of an exceptional point for quantum evolution and decoherence are hitherto unexplored. Here, we use post-selection on a three-level superconducting transmon circuit with tunable Rabi drive, dissipation, and detuning to carry out quantum state tomography of a single dissipative qubit in the vicinity of its exceptional point. Quantum state tomography reveals the PT symmetry breaking transition at zero detuning, decoherence enhancement at finite detuning, and a quantum signature of the exceptional point in the qubit relaxation state. Our observations demonstrate rich phenomena associated with non-Hermitian physics such as non-orthogonality of eigenstates in a fully quantum regime and open routes to explore and harness exceptional point degeneracies for enhanced sensing and quantum information processing.

Graphene, a single sheet of graphite with honeycomb lattice structure, has massless carriers with tunable density and polarity. We investigate the ground state phase diagram of two graphene sheets (embedded in a dielectric) separated by distance $d$ where the top layer has electrons and the bottom layer has holes, using mean-field theory. We find that a uniform excitonic condensate occurs over a large range of carrier densities and is weakly dependent on the relative orientation of the two sheets. We obtain the excitonic gap, quasiparticle energy and the density of states. We show that both, the condensate phase stiffness and the mass of the excitons, with massless particles as constituents, vary as the square-root of the carrier density, and predict that the condensate will not undergo Wigner crystallization.Comment: 4 pages, 3 figures; substantial text revisio

We study the phase-diagram of a parity and time-reversal (PT ) symmetric tight-binding chain with N sites and hopping energy J, in the presence of two impurities with imaginary potentials ±iγ located at arbitrary (P-symmetric) positions (m,m = N + 1 − m) on the chain where m ≤ N/2.We find that except in the two special cases where impurities are either the farthest or the closest, the PT -symmetric region -defined as the region in which all energy eigenvalues are real -is algebraically fragile. We analytically and numerically obtain the critical impurity potential γ P T and show that γ P T ∝ 1/N → 0 as N → ∞ except in the two special cases. When the PT symmetry is spontaneously broken, we find that the maximum number of complex eigenvalues is given by 2m. When the two impurities are the closest, we show that the critical impurity strength γ P T in the limit N → ∞ approaches J (J/2) provided that N is even (odd). For an even N the PT symmetry is maximally broken whereas for an odd N , it is sequentially broken. Our results show that the phase-diagram of a PT -symmetric tight-binding chain is extremely rich and that, in the continuum limit, this model may give rise to new PT -symmetric Hamiltonians. * yojoglek@iupui.edu

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including HCS, SO, HNCO, HFHF, N and P. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in HO. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

Bilayer electron-hole systems, where the electrons and holes are created via doping and are confined to separate layers, undergo excitonic condensation when the distance between the layers is smaller than the typical distance between the particles within the layer. We argue that the excitonic condensate is a novel dipolar superfluid in which the phase of the condensate couples to the gradient of the vector potential. We predict the existence of a dipolar supercurrent which can be tuned by an in-plane magnetic field. Thus the dipolar superfluid offers an example of excitonic condensate in which the composite nature of its constituent excitons is manifest in the macroscopic superfluid state. We also discuss various properties of this superfluid including the role of vortices.

We investigate the effects of a time-periodic, non-hermitian, PT -symmetric perturbation on a system with two (or few) levels, and obtain its phase diagram as a function of the perturbation strength and frequency. We demonstrate that when the perturbation frequency is close to one of the system resonances, even a vanishingly small perturbation leads to PT symmetry breaking. We also find a restored PT -symmetric phase at high frequencies, and at moderate perturbation strengths, we find multiple frequency windows where PT -symmetry is broken and restored. Our results imply that the PT -symmetric Rabi problem shows surprisingly rich phenomena absent in its hermitian or static counterparts. Introduction.A two-level system coupled to a sinusoidally varying potential is a prototypical example of a time-dependent, exactly solvable Hamiltonian, with profound implications to atomic, molecular, and optical physics [1]. When the frequency of perturbation ω is close to the characteristic frequency ∆ of the two-level system -near resonance -the system undergoes complete population inversion for an arbitrarily small strength γ of the potential [2]. The implications of this result to spin magnetic resonance, Rabi flopping [3], and its generalization, namely the Jaynes-Cummings model [4,5], have been extensively studied over the past half century [6,7]. Surprisingly, the quantum Rabi problem, where the full quantum nature of the perturbing bosonic field is taken into account, has only been recently solved [8].The two-level model is useful because it is applicable to many-level systems when the perturbation frequency is close to or resonant with a single pair of levels. As the detuning away from resonance |∆ − ω| increases, the perturbation strength necessary for population inversion increases linearly with it; in a many-level system, with increased potential strength, transitions to other levels have to be taken into account and the resultant problem is not exactly solvable. Therefore, understanding the behavior of a system in the entire parameter space (γ, ω) requires analytical and numerical approaches. All of these studies are restricted to hermitian potentials.In recent years, discrete Hamiltonians with a hermitian tunneling term H 0 and a non-hermitian perturbation V that are invariant under combined parity and timereversal (PT ) operations have been extensively investigated [9][10][11][12][13][14][15][16]. The spectrum λ of a PT -symmetric Hamiltonian is real when the strength γ of the non-hermitian perturbation is smaller than a threshold γ P T set by the hermitian tunneling term. Traditionally, the emergence of complex-conjugate eigenvalues that occurs when the threshold is exceeded, γ > γ P T , is called PT symmetry breaking [17][18][19]. It is now clear that PT -symmetric Hamiltonians represent open systems with balanced gain and loss, and PT symmetry breaking is a transition from a quasiequilibrium state (PT -symmetric state) to