We study the dynamics of a two-level impurity embedded in a two-dimensional Bose-Hubbard model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular, we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the Bose-Hubbard environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method [Phys. Rev. Research 2, 033276 (2020)] - closely related to slave boson approaches - that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.
We analyze the dephasing dynamics of an impurity coupled to an anharmonic environment. We show that a strong anharmonicity produces two different effects depending on the environment temperature: for high temperatures, the system suffers a strong dephasing, while for low temperatures there is a strong information back-flow (as measured by the Breuer-Laine-Piilo (BLP) non-Markovianity measure). Both dephasing and back-flow are particularly significant when the anharmonic potential allows environment states very close to the dissociation limit. In contrast, the information back-flow is suppresse…
We investigate the influence of a Bose-Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the quantum master equation reproduces the exact evolution of the qubits. We characterise the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and superdecoherence is observabl…
We investigate Bose-Hubbard chains in a central depleted well configuration, with dephasing in the middle well. We look at equilibration of populations, pseudo-entropy, and entanglement measures. Using stochastic integration in the truncated Wigner representation, we find that the initial quantum states of the occupied wells has an influence on the subsequent dynamics, and that with more than three wells, the chains do not reach a full equilibrium, with edge effects becoming important, and the time to reach the steady state becoming longer. The evolutions with and without phase diffusion are q…
We report Ramsey spectroscopy on the clock states of individual Cs impurities immersed in an ultracold Rb bath. We record both the interaction-driven phase evolution and the decay of fringe contrast of the Ramsey interference signal to obtain information about bath density or temperature nondestructively. The Ramsey fringe is modified by a differential shift of the collisional energy when the two Cs states superposed interact with the Rb bath. This differential shift is directly affected by the mean gas density and the details of the Rb-Cs interspecies scattering length, affecting the phase ev…
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the BEC. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realisable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of superfluid and Mott insulator, respectively…
We construct an exact map between a tight-binding model on any bipartite lattice in presence of dephasing noise and a Hubbard model with imaginary interaction strength. In one dimension, the exact many-body Liouvillian spectrum can be obtained by application of the Bethe ansatz method. We find that both the non-equilibrium steady state and the leading decay modes describing the relaxation at late times are related to the eta-pairing symmetry of the Hubbard model. We show that there is a remarkable relation between the time-evolution of an arbitrary k-point correlation function in the dissipati…
The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $η$ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the cha…
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.
We show how impurity atoms can measure moments of ultracold atomic gas densities, using the example of bosons in a one-dimensional lattice. This builds on a body of work regarding the probing of systems by measuring the dephasing of an immersed qubit. We show this dephasing is captured by a function resembling characteristic functions of probability theory, of which the derivatives at short times reveal moments of the system operator to which the qubit couples. For a qubit formed by an impurity atom, in a system of ultracold atoms, this operator can be the density of the system at the location…
We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V> 0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion H$^-$ problem. There are several different types of bound states in this system, each of which appears in a specific region. For given $V$, there exists a (positive) critical value $U_{c1}$ of $U$, below which the ground state is a bound state. Interestingly, close to the critical value ($U\lesssim U_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function,…
We study a two-level impurity coupled locally to a quantum gas on an optical lattice. For state-dependent interactions between the impurity and the gas, we show that its evolution encodes information on the local excitation spectrum of gas at the coupling site. Based on this, we design a nondestructive method to probe the system's excitations in a broad range of energies by measuring the state of the probe using standard atom optics methods. We illustrate our findings with numerical simulations for quantum lattice systems, including realistic dephasing noise on the quantum probe, and discuss p…
We analyze Josephson's oscillation of Bose particles in the open (dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum state into a state suitable for observing the oscillation by using a special protocol for external driving. Next, we switch off the driving and observe the oscillation. It is shown that the main mechanism for the decay of Josephson's oscillation is the dephasing due to fluctuating number of particles in open systems. An analytical estimate for the decay time is obtained.
We report the first theoretical estimate of the nuclear-spin dephasing time T_2 owing to the spin interaction with the two-dimensional electron gas, when the latter is in the integer quantum Hall state, in a two-dimensional heterojunction or quantum well at low temperature and in large applied magnetic field. We establish that the leading mechanism of dephasing is due to the impurity potentials that influence the dynamics of the spin via virtual magnetic spin-exciton scattering. Implications of our results for implementation of nuclear spins as quantum bits (qubits) for quantum computing are d…
A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry can be obtained with a generalized Bethe ansatz if periodic boundary conditions are imposed. Furthermore, we provide numerical evidence that this holds true for open boundary conditions as well. The model exhibits backscattering at the impurity site -- which usually destroys integrability -- yet there exists an integrable subspace. We investigate the non-inte…
Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in t…
We consider the dephasing of two internal states |0> and |1> of a trapped impurity atom, a so-called atomic quantum dot (AQD), where only state |1> couples to a Bose-Einstein condensate (BEC). A direct relation between the dephasing of the internal states of the AQD and the temporal phase fluctuations of the BEC is established. Based on this relation we suggest a scheme to probe BEC phase fluctuations nondestructively via dephasing measurements of the AQD. In particular, the scheme allows to trace the dependence of the phase fluctuations on the trapping geometry of the BEC.
We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization)…
Site-occupation embedding theory (SOET) is an alternative formulation of density-functional theory (DFT) for model Hamiltonians where the fully-interacting Hubbard problem is mapped, in principle exactly, onto an impurity-interacting (rather than a non-interacting) one. It provides a rigorous framework for combining wavefunction (or Green function) based methods with DFT. In this work, exact expressions for the per-site energy and double occupation of the uniform Hubbard model are derived in the context of SOET. As readily seen from these derivations, the so-called bath contribution to the per…
We present a model of two Anderson impurities coupled to and through a superconducting island. The model parametrizes the strength of the coupling between impurity sites, allowing it to represent a variable distance between the impurities. We systematically explore the effect of the model parameters in the subspaces with total even and odd occupancy, identifying unique features of the charge stability diagrams that distinguish the two parities. For total odd electron parity, we identify a device tuning, in which the splitting between the two lowest energy states is highly insensitive to change…
