It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped in these networks with different kinds of coupling strengths between them. Particularly, by taking the underlying networks of so called group schemes as interacting boson networks, we show how choose suitable coupling strengths between the nodes, in order that an arbitrary qudit state be transferred from one node to its antipode, perfectly. In fact, by employing the group theory properties of these networks, an explicit formula for suitable coupling strengths has been given in order that perfect state transfer (PST) be achieved. Finally, as examples, PST on the underlying networks associated with cyclic group C2m, dihedral group D2n, Clifford group CL(n), and the groups U6n and V8n has been considered in details. Keywords: Bose-Hubbard Hamiltonian, Interacting boson networks, Perfect state transfer (PST), Qudit state, Underlying networks, Group schemes PACs Index: 01.55.+b, 02.10.Yn
A famously hard graph problem with a broad range of applications is computing the number of perfect matchings, that is the number of unique and complete pairings of the vertices of a graph. We propose a method to estimate the number of perfect matchings of undirected graphs based on the relation between Gaussian Boson Sampling and graph theory. The probability of measuring zero or one photons in each output mode is directly related to the hafnian of the adjacency matrix, and thus to the number of perfect matchings of a graph. We present encodings of the adjacency matrix of a graph into a Gauss…
We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical lattices or polaritons in on-chip coupled cavities. Significantly, a family of Hamiltonians, both linear and nonlinear, is found which are related to the Bose-Hubbard model and that enable the perfect transfer of arbitrary functions. It is shown that the state transfer between two sites in two-dimensional lattices can result in quantum interference due to the …
We show how to achieve perfect quantum state transfer and construct effective two-qubit gates between distant sites in engineered bosonic and fermionic networks. The Hamiltonian for the system can be determined by choosing an eigenvalue spectrum satisfying a certain condition, which is shown to be both sufficient and necessary in mirror-symmetrical networks. The natures of the effective two-qubit gates depend on the exchange symmetry for fermions and bosons. For fermionic networks, the gates are entangling (and thus universal for quantum computation). For bosonic networks, though the gates are…
We find analytic models that can perfectly transfer, without state initializati$ or remote collaboration, arbitrary functions in two- and three-dimensional interacting bosonic and fermionic networks. We elaborate on a possible implementation of state transfer through bosonic or fermionic atoms trapped in optical lattices. A significant finding is that the state of a spin qubit can be perfectly transferred through a fermionic system. Families of Hamiltonians, both linear and nonlinear, are described which are related to the linear Boson model and that enable the perfect transfer of arbitrary fu…
We investigate the most general conditions under which a finite ferromagnetic long-range inter- acting spin chain achieves unitary fidelity and the shortest transfer time in transmitting an unknown input qubit. A deeper insight into system dynamics, allows us to identify an ideal system involving sender and receiver only. However, this two-spin ideal chain is unpractical due to the rapid decrease of the coupling strength with the distance. Therefore, we propose an optimization scheme for ap- proaching the ideal behaviour, while keeping the interaction strength still reasonably high. The proced…
In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbor resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides…
A duality between the properties of many spinor bosons on a regular lattice and those of a single particle on a weighted graph reveals that a quantum particle can traverse an infinite hierarchy of networks with perfect probability in polynomial time, even as the number of nodes increases exponentially. The one-dimensional `quantum wire' and the hypercube are special cases in this construction, where the number of spin degrees of freedom is equal to one and the number of particles, respectively. An implementation of near-perfect quantum state transfer across a weighted parallelepiped with ultra…
The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs…
Bosonic degrees of freedom and their emergence as a part of complex quantum many-body dynamics, symmetries, collective behavior, clustering and phase transitions play an important role in modern studies of quantum systems. In this work we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.
The correct form of the Schmidt decomposition of the stationary wave functions for a system of two interacting particles trapped in a two-dimensional harmonic potential is given
We study the scattering of a matter-wave from an interacting system of bosons in an optical lattice, focusing on the strong-interaction regime. Analytical expressions for the many-body scattering cross section are derived from a strong-coupling expansion and a site-decoupling mean-field approximation, and compared to numerically obtained exact results. In the thermodynamic limit, we find a non-vanishing inelastic cross section throughout the Mott insulating regime, which decays quadratically as a function of the boson-boson interaction.
We investigate the properties of strongly interacting heteronuclear boson-boson mixtures loaded in realistic optical lattices, with particular emphasis on the physics of interfaces. In particular, we numerically reproduce the recent experimental observation that the addition of a small fraction of K induces a significant loss of coherence in Rb, providing a simple explanation. We then investigate the robustness against the inhomogeneity typical of realistic experimental realizations of the glassy quantum emulsions recently predicted to occur in strongly interacting boson-boson mixtures on idea…
Computing the ground-state energy of interacting electron (fermion) problems has recently been shown to be hard for QMA, a quantum analogue of the complexity class NP. Fermionic problems are usually hard, a phenomenon widely attributed to the so-called sign problem occurring in Quantum Monte Carlo simulations. The corresponding bosonic problems are, according to conventional wisdom, tractable. Here, we discuss the complexity of interacting boson problems and show that they are also QMA-hard. In addition, we show that the bosonic version of the so-called N-representability problem is QMA-comple…
We study the scattering of matter-waves from interacting bosons in a one-dimensional optical lattice, described by the Bose-Hubbard Hamiltonian. We derive analytically a formula for the inelastic cross section as a function of the atomic interaction in the lattice, employing Bogoliubov's formalism for small condensate depletion. A linear decay of the inelastic cross section for weak interaction, independent of number of particles, condensate depletion and system size, is found.
We compute the pair entanglement between two interacting bosons in a two dimensional (2D)isotropic harmonic trap. The interaction potential is modeled by a 2D regularized pseudo-potential. By analytically decomposing the wave function into the single particle basis, we show the dependency of the pair entanglement on the scattering length. Our results turn out to be in good agreements with earlier results using a quasi-2D geometry.
We explore the conditions under which identical particles in unitary linear networks behave as the other species, i.e. bosons as fermions and fermions as bosons. It is found that the Boson-Sampling computer of Aaronson & Arkhipov can be implemented in an interference experiment with non-interacting fermions in an appropriately entangled state. Moreover, a scheme is proposed which simulates the scattershot version of the Boson-Sampling computer by preparing, on the fly, the required entangled state of fermions from an unentangled one.
We develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. We show how collisional energy transfer between the bosons induces the thermalization of the inelastic single-particle current which, after only few collision events, dominates over the elastic contribution described by the Gross-Pitaevskii ansatz.
We study the quantum phase transitions of a model that describes the interconversion of interacting bosonic atoms and molecules. Using a classical analysis, we identify a threshold coupling line separating a molecular phase and a mixed phase. Through studies of the energy gap, von Neumann entanglement entropy, and fidelity, we give evidence that this line is associated to a boundary line in the ground-state phase diagram of the quantum system.
We study theoretically quantum dynamics of interacting bosons in artificial magnetic fields as engineered in recent ultracold atomic experiments, where quantum cyclotron orbital motion has been observed. With exact numerical simulations and perturbative analyses, we find that interactions induce damping in the cyclotron motion. The damping time is found to be dependent on interaction and tunneling strengths monotonically, while its dependence on magnetic flux is non-monotonic. Sufficiently strong interactions would render bosons dynamically localized inhibiting the cyclotron motion. The dampin…
We study spatial correlation functions of local operators of interacting many bosons confined in a box of a large, but volume V, for various `ground states' whose energy densities are almost degenerate. The ground states include the coherent state of interacting bosons (CSIB), the number state of interacting bosons (NSIB), and the number-phase squeezed state of interacting bosons, which interpolates between the CSIB and NSIB. It was shown previously that only the CSIB is robust (i.e., does not decohere for a macroscopically long time) against the leakage of bosons into an environment. We show …
The quantum kicked rotor is well-known to display dynamical localization in the non-interacting limit. In the interacting case, while the mean-field (Gross-Pitaevskii) approximation displays a destruction of dynamical localization, its fate remains debated beyond mean-field. Here we study the kicked Lieb-Liniger model in the few-body limit. We show that for any interaction strength, two kicked interacting bosons always dynamically localize, in the sense that the energy of the system saturates at long time. However, contrary to the non-interacting limit, the momentum distribution $Π(k)$ of the …
We describe basic types of free fields (1) neutral scalar bosons; (2) massive vector bosons; (3) massless vector bosons; (4) charged scalar bosons; (5) Dirac fermions; (6) Majorana fermions. We also consider free field perturbed by a linear or quadratic perturbation involving a classical (c-number) function: (1) neutral scalar bosons interacting with a linear source; (2) neutral scalar bosons interacting with a mass-like perturbation; (3) massive photons interacting with an classical current; (4) massless photons interacting with an classical current. (5) charged scalar bosons interacting with…
We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose-Hubbard model and solve the problem numerically by means of the exact diagonalization (ED) method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator (MI) transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces …
We study the dynamics of a strongly interacting bosonic quantum gas in an optical lattice potential under the effect of a dissipative environment. We show that the interplay between the dissipative process and the Hamiltonian evolution leads to an unconventional dynamical behavior of local number fluctuations. In particular we show, both analytically and numerically, the emergence of an anomalous diffusive evolution in configuration space at short times and, at long times, an unconventional dynamics dominated by rare events. Such rare events, common in disordered and frustrated systems, are du…
Any {\it exact} eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a {\it symmetry-broken} function $Φ$. For two particles, we solve the problem {\it exactly} for all energy levels and any inter-particle interaction. Especially for the ground-state, $Φ$ is given by the simple Hartree-Fock/Hartree ansatz for fermions/bosons. Implications for several and many particles as well as a numerical example are provided.
The study of topological effects in physics is a hot area, and only recently researchers were able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multi-particle and interaction effects. Here, we introduce multi-particle Wannier states for interacting systems with co-translational symmetry. We reveal how the shift of multi-particle Wannier state relates to the multi-particle Chern number, and study the two-boson Thouless pumping in an interacting Rice-Mele model. In addition to the bound-state Thouless pump…
We investigate the finite-size scaling exponents for the critical point at the shape phase transition from U(5) (spherical) to O(6) (deformed $γ$-unstable) dynamical symmetries of the Interacting Boson Model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading order correction to the ground state energy, the gap, the expectation value of the $d$-boson number in the ground state and the $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scal…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for repulsive particles and a super-threshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a sub-threshold trap a collective bound state always forms for a sufficiently large number of bosons despite the inability of interpa…
We study the quantum phase transition mechanisms that arise in the Interacting Boson Model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.
We investigate the mechanism in the tunneling dynamics of open ultracold few-boson systems by numerically solving the time-dependent few-boson Schrödinger equation exactly. By starting from a weakly repulsive, initially coherent two-boson system we demonstrate that the decay dynamics incorporate fragmentation. The wavefunction of the tunneling state exhibits a pronounced dynamically-stable pattern which we explain by an analytical model. By studying more bosons and stronger interactions we arrive to the conclusion that the decay by tunneling is not a coherent process and exhibits a wealth of p…
We study the robustness, against the leakage of bosons, of wave functions of interacting many bosons confined in a finite box, by deriving and analyzing a general equation of motion for the reduced density operator. We identify a robust wave function that remains a pure state, whereas other wave functions, such as the Bogoliubov's ground state and the ground state with a fixed number of bosons, evolve into mixed states. Although these states all have the off-diagonal long-range order, and almost the same energy densities, we argue that only the robust state is realized as a macroscopic quantum…
A general time-dependent projection technique is applied to the study of the dynamics of quantum correlations in a system consisting of interacting fermionic and bosonic subsystems, described by the Jaynes-Cummings Hamiltonian. The amplitude modulation of the Rabi oscillations which occur for a strong, coherent initial bosonic field is obtained from the spin intrinsic depolarization resulting from collisional corrections to the mean-field approximation.
