We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of these are the one-sided and alternative ones. Using the differences between coin states of the individual component, we can simulate the third case in which both components have identical probability profiles. We also observe that the mutual information transfer between two components of the walk is minimized when this difference across the two sides of the ladder is maximized.
We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 i…
The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in anyonic quantum walks in quasi-one dimensional ladder geometries. For anyons which correspond to spin-1/2 irreps of the quantum groups $SU(2)_k$, the non-Abelian species $(1<k<\infty)$ gives rise to entanglement between the walker and topological degrees of freedom which is quantified by quantum link invariants over the trajectories of the walk. The decoherence…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance between source and target or adding redundant branches to the actual graph may surprisingly result in a significant enhancement of transport efficiency. We explain analytically the observed non-classical effects using the concept of trapped states for several intriguing geometries including the ladder graph, the Cayley tree and its modifications.
The singularity of quantum correlations, such as quantum entanglement(QE) and quantum discord(QD), has been widely regarded as a valuable indicator for quantum phase transition(QPT) in low-dimensional quantum systems. In this paper, for a spin ladder system with ring exchange, we find that the singularity of QD (or QE) could not indicate the critical points of the system. Instead, the QD shows a novel odd-even effect in some phases, which can be used to detect the phase boundary points. The size effect is related to the symmetry breaking of the ladder.
We show that various kinds of one-photon quantum states studied in the field of quantum optics admit ladder operator formalisms and have the generally deformed oscillator algebraic structure. The two-photon case is also considered. We obtain the ladder operator formalisms of two general states defined in the even/odd Fock space. The two-photon states may also have a generally deformed oscillator algebraic structure. Some interesting examples of one-photon and two-photon quantum states are given.
The ladder operators for one dimensional quantum harmonic oscillator were constructed by Schrödinger in 1940s. We extend this method to a two dimensional uniform magnetic field and establish the ladder operators which depend on all spatial variables of quantum system. The Hamiltonian of quantum system can also be written by the velocity of the particle.
The fidelity susceptibility and entanglement entropy in a system of two-leg $XXZ$ spin ladder with rung coupling is investigated by using exact diagonalization of the system. The effects of rung coupling on fidelity susceptibility, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition between two different $XY$ phases can be well characterized by the fidelity susceptibility. Though the quantum phase transition from $XY$ phase to rung singlet phase can be hardly detected by fidelity susceptibility, it can be predicted by the first derivati…
A criterion for strong coupling between two quantum emitters and a single resonant light mode in a cavity is presented. The criterion takes into account the escape of cavity photons and the spontaneous emission of the emitters, which are modeled as two level systems. By using such criterion, the dissipative Tavis-Cummings ladder of states is constructed, and it is shown that the inclusion of one more emitter with respect to the Jaynes-Cummings (single emitter) case increases the effective parameter region in which $n^{\text{th}}$ order Rabi splitting is observed.
We investigate the photon induced tunneling phenomena in a photonic crystal cavity containing a strongly coupled quantum dot and describe how this tunneling can be used to generate photon states consisting mainly of a particular Fock state. Additionally, we study experimentally the photon-induced tunneling as a function of excitation laser power and frequency and show the signature of second rung of the Jaynes-Cummings Hamiltonian in the observed photon-statistics.
We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The invers…
The two-photon ladder climbing (successive two-photon Landau-Zener-type transitions) in a chirped quantum nonlinear oscillator and its classical limit (subharmonic autoresonance) are discussed. An isomorphism between the chirped quantum-mechanical one and two-photon resonances in the system is used in calculating the threshold for the phase-locking transition in both the classical and quantum limits. The theory is tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space.
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse potential. The operators are a representation of the shifting energy levels of the states exhibited by the wavefunction. From this result, we manipulate and deform the operators in such a way that it gives a noncommutative property to promote noncommutative quantum mechanics (NCQM). The resultant NC feature can be shown in the spatial coordinates and finally th…
We propose a novel quantum electrodynamics (QED) platform where quantum emitters interact with a Hofstadter-ladder waveguide. We demonstrate several intriguing phenomena stemming from the exotic dispersion relation and vacuum mode properties led by the effective spin-orbit coupling, which have no analog in other QED setups. First, by assuming emitter's frequency to be resonant with the lower band, we find that the spontaneous emission is chiral with most photonic field decaying unidirectionally. Both numerical and analytical results indicate that the Hofstadter-ladder waveguide can be engineer…
Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more exotic quantum mechanical degrees of freedom, so-called non-Abelian anyons, which can be thought of as certain quantum deformations of ordinary SU(2) spins. Such non-Abelian anyons occur as quasiparticle excitations in topological quantum fluids, including p_x + i p_y superconductors, certain fractional quantum Hall states, and rotating Bose-Einstein condensat…
We investigate quantum phase transitions in ladders of spin 1/2 particles by engineering suitable matrix product states for these ladders. We take into account both discrete and continuous symmetries and provide general classes of such models. We also study the behavior of entanglement of different neighboring sites near the transition point and show that quantum phase transitions in these systems are accompanied by divergences in derivatives of entanglement.
We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size …
Motivated by the recent discovery of ergodicity breaking in geometrically frustrated systems, we study the quench dynamics of interacting hardcore bosons on a sawtooth ladder. We identify a set of initial states for which this system exhibits characteristic signatures of localization like initial state memory retention and slow growth of entanglement entropy for a wide parameter regime. Remarkably, this localization persists even when the many-body spectrum is thermalizing. We argue that the localized dynamics originates from an interaction induced quantum interference. Our results show that t…
An interesting aspect of antiferromagnetic quantum spin ladders, with complete dimer coverings, is that the wave function can be recursively generated by estimating the number of coverings in the valence bond basis, which follow the fabled Fibonacci sequence. In this work, we derive generalized forms of this sequence for multi-legged and doped quantum spin ladders, which allow the corresponding dimer-covered state to be recursively generated. We show that these sequences allow for estimation of physically and information-theoretically relevant quantities in large spin lattices without resortin…
We investigate finite-size scaling of genuine multisite entanglement in the ground state of quantum spin-1/2 Heisenberg ladders. We obtain the ground states of odd- and even-legged Heisenberg ladder Hamiltonians and compute genuine multisite entanglement, the generalized geometric measure (GGM), which shows that for even rungs, GGM increases for odd-legged ladder while it decreases for even ones. Interestingly, the ground state obtained by short-range dimer coverings, under the resonating valence bond (RVB) ansatz, encapsulates the qualitative features of GGM for both the ladders. We find that…
We investigate the degree of indistinguishability of cascaded photons emitted from a 3-level quantum ladder system; in our case the biexciton-exciton cascade of semiconductor quantum dots. For the 3-level quantum ladder system we theoretically demonstrate that the indistinguishability is inherently limited for both emitted photons and determined by the ratio of the lifetimes of the excited and intermediate states. We experimentally confirm this finding by comparing the quantum interference visibility of non-cascaded emission and cascaded emission from the same semiconductor quantum dot. Quantu…
We formulate an analytical recursive method to generate the wave function of doped short-range resonating valence bond (RVB) states as a tool to efficiently estimate multisite entanglement as well as other physical quantities in doped quantum spin ladders. We prove that doped RVB ladder states are always genuine multipartite entangled. Importantly, our results show that within specific doping concentration and model parameter regimes, the doped RVB state essentially characterizes the trends of genuine multiparty entanglement in the exact ground states of the Hubbard model with large onsite int…
We investigate the behavior of persistent currents for a fixed number of noninteracting fermions in a periodic quantum ladder threaded by Aharonov-Bohm and transverse magnetic fluxes $Φ$ and $χ$. We show that the coupling between ladder legs provides a way to effectively change the ground-state fermion-number parity, by varying $χ$. Specifically, we demonstrate that varying $χ$ by $2π$ (one flux quantum) leads to an apparent fermion-number parity switch. We find that persistent currents exhibit a robust $4π$ periodicity as a function of $χ$, despite the fact that $χ\to χ+ 2π$ leads to modifica…
We explore the physical mechanism to coherently transfer the quantum information of spin by connecting two spins to an isotropic antiferromagnetic spin ladder system as data bus. Due to a large spin gap existing in such a perfect medium, the effective Hamiltonian of the two connected spins can be archived as that of Heisenberg type, which possesses a ground state with maximal entanglement. We show that the effective coupling strength is inversely proportional to the distance of the two spins and thus the quantum information can be transferred between the two spins separated by a longer distanc…
Bipartite entanglement measures are fantastic tools to investigate quantum phases of correlated electrons. Here, I analyze the entanglement spectrum of **gapped** two-leg quantum Heisenberg ladders on a periodic ribbon partitioned into two identical periodic chains. Comparison of various entanglement entropies proposed in the literature is given. The entanglement spectrum is shown to closely reflect the low-energy gapless spectrum of each individual edge, for any sign of the exchange coupling constants. This extends the conjecture initially drawn for Fractional Quantum Hall systems to the fiel…
Quantum simulations would be highly desirable in order to investigate the finite density physics of QCD. $(1+1)$-d $\mathbb{C}P(N-1)$ quantum field theories are toy models that share many important features of QCD: they are asymptotically free, have a non-perturbatively generated massgap, as well as $θ$-vacua. $SU(N)$ quantum spin ladders provide an unconventional regularization of $\mathbb{C}P(N-1)$ models that is well-suited for quantum simulation with ultracold alkaline-earth atoms in an optical lattice. In order to validate future quantum simulation experiments of $\mathbb{C}P(2)$ models a…
We investigate the quantum-critical behavior between the rung-singlet phase with hidden string order and the Néel phase with broken $SU(2)$-symmetry on quantum spin ladders with algebraically decaying unfrustrated long-range Heisenberg interactions. Combining perturbative continuous unitary transformations (pCUT) with a white-graph expansion and Monte Carlo simulations yields high-order series expansions of energies and observables in the thermodynamic limit about the isolated rung-dimer limit. The breakdown of the rung-singlet phase allows to determine the critical line and the entire set of …
Observation of magnetic quantum phase crossovers in a semiconductor spin ladder
QuTech and Kavli Institute of Nanoscience, Delft University of Technology（代尔夫特理工大学奎克研究所和纳米科学卡弗里研究所）；IBM Quantum, IBM Research – Zurich（IBM量子，IBM研究-苏黎世）；Department of Physics and Astronomy, University College London（伦敦大学学院物理与天文学系）；Netherlands Organisation for Applied Scientific Research (TNO)（荷兰应用科学研究组织（TNO））
We consider a two-chain, spin-1/2 antiferromagnetic Heisenberg spin ladder in an external magnetic field H. The spin ladder is known to undergo second order quantum phase transitions (QPTs) at two critical values, Hc1 and Hc2, of the magnetic field. There are now known examples of strongly coupled (rung exchange interaction much stronger than nearest-neighbour intrachain exchange interaction) organic ladder compounds in which QPTs have been experimentally observed. In this paper, we investigate whether well-known bipartite entanglement meaures like one-site von Neumann entropy, two-site von Ne…
A resonating valence bond (RVB) state of a lattice of quantum systems is a potential resource for quantum computing and communicating devices. It is a superposition of singlet, i.e., dimer, coverings - often restricted to nearest-neighbour ones - of the lattice. We develop a polynomial representation of multipartite quantum states to prove that RVB states on ladder lattices possess genuine multipartite entanglement. The multipartite entanglement of doped RVB states and RVB states that are superposed with varying weights for singlet coverings of ladder lattices can both be detected by using thi…
A new kind of regular quasienergy (Floquet) spectrum is found for the generalized kicked particle under quantum-resonance conditions at generic quasimomentum, a quantity most relevant in atom-optics experimental realizations of kicked-rotor systems. The new non-Poisson regular spectrum has the structure of a staggered ladder, i.e., it is the superposition of a finite number of ladder subspectra all having the same spacing, which is independent of the nonintegrability of the system. This spectral structure is shown to have distinct quantum-dynamical manifestations: A suppression of quantum reso…
We report on the discovery of a quantum tri-critical point (QTP) separating a line of first-order topological quantum phase transitions from a continuous transition regime in a strongly correlated one-dimensional lattice system. Specifically, we study a fermionic four-leg ladder supporting a symmetry-protected topological phase in the presence of on-site interaction, which is driven towards a trivial gapped phase by a nearest-neighbor interaction. Based on DMRG simulations, we show that, as a function of the interaction strength, the phase transition between the topological and the trivial pha…
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of `valence bands' in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are…
