We study the ground state phase diagram of a one-dimensional two qubits Dicke-Hubbard model with XY qubit-qubit interaction. We use a numerical method combing the cluster mean-field theory and the matrix product state(MPS) to obtain the exact wave function of the ground state. When counter-rotating wave terms(CRTs) in the qubit-cavity coupling are neglected, we observe a rich phase diagram including a quantum phase transition between the Mott-insulating phase and the superfluid phase. This phase transition can be either the first-order or the second-order type depending on whether the total angular momentum changes across the phase diagram. Moreover, we observe two quantum triple points, at which three different phases coexist, with both positive and negative XY interactions. By further considering the effect of CRTs, we find that the main feature in the previous phase diagram, including the existence of quantum triple points, is retained. We also show that CRTs extremely demolish the non-local correlations in the coherent phase.
We investigate the ground state behavior of the Dicke-Hubbard model including counter-rotating-terms. By generalizing an extended coherent state approach within mean-field theory, we self-consistently obtain the ground state energy and delocalized order parameter. Localization-delocalization quantum phase transition of photons is clearly observed by breaking the parity symmetry. Particularly, Mott lobes are fully suppressed, and the delocalized order parameter shows monotonic enhancement by increasing qubit-cavity coupling strength, in sharp contrast to the Dicke-Hubbard model under rotating-w…
We extend the idea of quantum phase transitions of light in atom-photon system with Dicke-Bose-Hubbard model for arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a self-consistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for arbitrary numb…
Recently, several schemes for the experimental creation of Dicke states were described. In this paper, we show that all the $n$-qubit symmetric Dicke states with $l$ ($2\leq l\leq (n-2)$) excitations are inequivalent to the $% |GHZ>$ state or the $|W>$ state under SLOCC, that the even $n$% -qubit symmetric Dicke state with $n/2$ excitations is inequivalent to any even $n$-qubit symmetric Dicke state with $l\neq n/2$ excitations under SLOCC, and that all the $n$-qubit symmetric Dicke states with $l$ ($2\leq l\leq (n-2)$) excitations satisfy Coffman, Kundu and Wootters' generalized monogamy ineq…
We discuss a general physical mechanism for arbitrary control of the quantum states of multiple qubits in the symmetric Dicke subspace. The qubit-qubit coupling leads to unequal energy spacing in the symmetric Dicke subspace. This allows one to manipulate a prechosen transition with an external driving source, with other transitions remaining off-resonant. Any entangled state in the symmetric Dicke subspace can be created from the initial ground state by tuning the driving source. We illustrate the idea in cavity QED, but it should be applicable to other related systems.
The impacts that the environment has on the quantum phase transition of light in the DickeBose-Hubbard model are investigated. Based on the quasibosonic approach, mean field theory and the perturbation theory, the formulation of the Hamiltonian, the eigenenergies and the superfluid order parameter are obtained analytically. Compared with the ideal cases, the order parameter of the system evolves with time as the photons naturally decay in their environment. When the system starts with the superfluid state, the dissipation makes the photons tend to localize, and a greater hopping energy of phot…
We report the first experimental generation and characterization of a six-photon Dicke state. The produced state shows a fidelity of F=0.56+/-0.02 with respect to an ideal Dicke state and violates a witness detecting genuine six-qubit entanglement by four standard deviations. We confirm characteristic Dicke properties of our resource and demonstrate its versatility by projecting out four- and five-photon Dicke states, as well as four-photon GHZ and W states. We also show that Dicke states have interesting applications in multiparty quantum networking protocols such as open-destination teleport…
We report the experimental demonstration of two quantum networking protocols, namely quantum 1->3 telecloning and open-destination teleportation, implemented using a four-qubit register whose state is encoded in a high-quality two-photon hyperentangled Dicke state. The state resource is characterized using criteria based on multipartite entanglement witnesses. We explore the characteristic entanglement-sharing structure of a Dicke state by implementing high-fidelity projections of the four-qubit resource onto lower-dimensional states. Our work demonstrates for the first time the usefulness of …
We determine the minimal number of qubits that it is necessary to have access to in order to transform Dicke states into other Dicke states. In general, the number of qubits in Dicke states cannot be increased via transformation gates by accessing only a single qubit, in direct contrast to other multipartite entangled states such as GHZ, W and cluster states. We construct a universal optimal gate which adds spin-up qubits or spin-down qubits to any Dicke state by minimal access. We also show the existence of a universal gate which transforms any size of Dicke state as long as it has access to …
Entanglement in multipartite quantum systems is much more elusive than its bipartite counterpart. In recent past the usefulness of multipartite entangled states in several information theoretic tasks have been demonstrated. Being a resource, the detection of multipartite entanglement is an imperative necessity. Among the different classes of multipartite entangled states the Dicke state has found importance in several tasks due to its permutation symmetric nature. In this work we propose a simple and elegant way of detecting n qubit Dicke states using permutation symmetric Bell operators. We c…
We give an analytical description of the dynamics of the three-qubit Dicke model using the adiabatic approximation in the parameter regime where the qubits transition frequencies are far off-resonance with the field frequency and the interaction strengths reach the ultra-strong coupling regimes. Qualitative differences arise when comparing to the single- and two-qubit systems - simple analytic formulas show that three revival sequences produce a three-frequency beat note in the time evolution of the population. We find an explicit way to estimate the dynamics for the qubit-field and qubit-qubi…
We discuss the Jaynes-Cummings-Hubbard model (JCHM) describing the superfluid-Mott insulator transition of polaritons (i.e., dressed photon-qubit states) in coupled qubit-cavity arrays in the crossover from strong to weak correlations. In the strongly correlated regime the phase diagram and the elementary excitations of lattice polaritons near the Mott lobes are calculated analytically using a slave boson theory (SBT). The opposite regime of weakly interacting polariton superfluids is described by a weak-coupling mean-field theory (MFT) for a generalised multi-mode Dicke model. We show that a …
We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.
We present a proposal for a probing scheme utilizing Dicke superradiance to obtain information about ultracold atoms in optical lattices. A probe photon is absorbed collectively by an ensemble of lattice atoms generating a Dicke state. The lattice dynamics (e.g., tunneling) affects the coherence properties of that Dicke state and thus alters the superradiant emission characteristics -- which in turn provides insight into the lattice (dynamics). Comparing the Bose-Hubbard and the Fermi-Hubbard model, we find similar superradiance in the strongly interacting Mott insulator regime, but crucial di…
We present a Dicke state preparation scheme which uses global control of $N$ spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state non-deterministically by collectively coupling the spins to an ancilla qubit via a $ZZ$-interaction, using $\ceil*{\log_2 N} + 1$ ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamon…
We try to classify the spectrum of the two-qubit Dicke model by calculating two quantum information measures of its eigenstates: the Wooters concurrence and the mutual quantum information. We are able to detect four spectral sets in each parity subspace of the model: one set is regular and given by the product of a Fock state of the field times the singlet Bell state of the qubits; the rest are fairly regular and related to the triplet states of the Bell basis. The singlet states become trapping states when we couple the Dicke model to an environment of harmonic oscillators, making them candid…
We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in n-qubit Dicke states with m-excitations. In a detailed analysis we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.
Pairwise correlation is really an important property for multi-qubit states. For the two-qubit X states extracted from Dicke states and their superposition states, we obtain a compact expression of the quantum discord by numerical check. We then apply the expression to discuss the quantum correlation of the reduced two-qubit states of Dicke states and their superpositions, and the results are compared with those obtained by entanglement of formation, which is a quantum entanglement measure.
The nonclassical feature of photons in the open finite-size Dicke model is investigated via the two-photon correlation function. The quantum dressed master equation combined with the extended coherent photonic states is applied to analyze the dissipative dynamics of both the photons and qubits. The anti-bunching to bunching transition of photons is clearly observed by tuning the qubit-photon coupling strength. The optimal qubits number is unraveled to enhance the two-photon correlation function. Moreover, the temperature bias of thermal baths induces significant two-photon bunching signature w…
We propose a fast and efficient technique to create classes of highly entangled states of trapped ions, such as arbitrary Dicke states and superpositions of them, e.g. NOON states. The ions are initialized in the phonon ground state and are addressed globally with a composite pulse that is resonant with the first motional sideband. The technique operates on comparatively short time scales, as resonant interactions allow one to use the minimum laser pulse area. The number of single pulses from the composite sequence is equal to the number of ions, thus the implementation complexity grows only l…
We study non-Markovian enhancement effects in the spontaneous emission of a collective excitation in a linear chain of up to 100 qubits coupled to a 1D waveguide. We find that for a critical separation of qubits, the system exhibits super-superradiant (SSR) behavior leading to collective decay stronger than the usual Dicke superradiance. Here, time-delayed coherent quantum feedback effects are at play on top of the usual Dicke superradiance effects. We find a linear scaling for the SSR decay rate with increasing qubit number $N$ such that $Γ_{\rm SSR} \sim 2.277 N γ_0$, where $γ_0$ is the sing…
In this work, we propose a method to investigate controllable qubit-resonator interactions in a Dicke model with driven biased term. The nonlinearity of spectrum, which can be induced by qubit-resonator interactions, plays an important role in such controllable interactions. To gain insight into mechanism of the nonlinearity, we perform a unitary transformation to the Hamiltonian. The results show that the nonlinearity of the transformed Hamiltonian depends on the qubit-resonator coupling strength. The general forms of the effective Hamiltonians are discussed in detail based on the frequency m…
We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zero-th order approximation gives correct solutions when the qubits are far detuned from the cavity. The first order approximation, called generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigen-solutions, we study both the bipartite entanglement and genuine multi…
Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although much attention has been attracted for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here, we propose efficient and practical protocols for verifying arbitrary $n$-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permut…
We propose a simple scheme for implementing quantum logic gates with a string of two-level trapped cold ions outside the Lamb-Dicke limit. Two internal states of each ion are used as one computational qubit (CQ) and the collective vibration of ions acts as the information bus, i.e., bus qubit (BQ). Using the quantum dynamics for the laser-ion interaction as described by a generalized Jaynes-Cummings model, we show that quantum entanglement between any one CQ and the BQ can be coherently manipulated by applying classical laser beams. As a result, universal quantum gates, i.e. the one-qubit rota…
We analyze the effect of position dependent excitation phase on the properties of entanglement between two qubits formed in atomic systems. We show that the excitation phase induces a vacuum mediated quantum interference in the system that affects the dynamical behavior of entanglement between the qubits. It is also found that the quantum interference leads to a coherent population transfer between the symmetric and antisymmetric states which can considerably modify the dynamics of two-qubit entanglement and can even prevent finite time disentanglement (sudden death) under certain conditions.
We study the ground state of a finite size ensemble of interacting qubits driven by a quantum field. We find a maximally entangled W-state in the ensemble part of the system for a certain coupling parameters region. The area of this region decreases as the ensemble size increases and, in the classical limit, becomes the line in parameter space that defines the phase transition of the system. In the classical limit, we also study the dynamics of the system and its transition from order to disorder for initial energies close to the ground state energy. We find that a critical energy providing th…
We obtain exact dynamics of a two-qubit central spin model (CSM) consisting of two interacting qubits homogeneously coupled to a spin bath via the $XXZ$-type coupling, with the bath initially prepared in linear superpositions of the symmetric Dicke states. Using the interaction picture Hamiltonian with respect to the non-spin-flipping part of the model, we derive a sequence of equations of motion within each magnetization sector satisfied by the probability amplitudes of the time-evolved state. These equations of motion admit analytical solutions for the single-qubit CSM in which one of the tw…
We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654$\pm$0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422$\pm$0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of …
We study genuine multipartite entanglement (GME) in a system of $n$ qubits prepared in symmetric Dicke states and subjected to the influences of noise. We provide general, setup-independent expressions for experimentally favorable tools such as fidelity- and collective spin-based entanglement witnesses, as well as entangled-class discriminators and multi-point correlation functions. Besides highlighting the effects of the environment on large qubit registers, we also discuss strategies for the robust detection of GME. Our work provides techniques and results for the experimental communities in…
Several sequential operations are usually needed for implementing controlled quantum gates and generating entanglement between a pair of quantum bits. Based on the conditional quantum dynamics for a two-ion system beyond the Lamb-Dicke limit, here we propose a theoretical scheme for manipulating two-qubit quantum information, i.e., implementing a universal two-qubit quantum gate and generating a two-qubit entangled state, by using a pair of simultaneous laser pulses. Neither the Lamb-Dicke approximation nor the auxiliary atomic level are required. The experimental realizability of this simple …
Symmetric ensembles of neutral atoms interacting via the Rydberg blockade are well-described by the Jaynes-Cummings Hamiltonian. We use this framework to study the problem of generating arbitrary superpositions of Dicke states of hyperfine qubits in such ensembles. The combination of the symmetric Rydberg blockade and microwaves that drive the qubits with a time-dependent phase is sufficient to make these ensembles completely controllable, in the sense that one can generate an arbitrary unitary transformation on the system. We apply this to the problem of state mapping. With currently feasible…
For certain {\it specific} (or {\it"magic"}) Lamb-Dicke (LD) parameters, Monroe {\it et al} showed [Phys. Rev. {\bf A 55}, R2489 (1997)] that a two-qubit quantum operation, between the external and internal degrees of freedom of a single trapped ion, could be implemented by applying a single carrier laser pulse. Here, we further show that, such a two-qubit operation (which is equivalent to the standard CNOT gate, only apart from certain phase factors) could also be significantly-well realized for {\it arbitrarily} selected LD parameters. Instead of the so-called "$π$-pulses" used in the previo…
We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of $N$ ion qubits that is prepared in a particular Fock state of motion, $|m>$. The $m$ phonons are removed by applying a laser pulse globally to the $N$ qubits, and converting the motional excitation to $m$ flipped spins. The global nature of this pulse ensures that the $m$ flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state $\D{N}{m}$. We calculate numerically the fidelity limits of the protocol an…
Data and code for collision-model Dicke-state preparation: depth-fidelity frontiers, circuit costs, and superconducting-processor measurements
Saint Louis University（圣路易斯大学）；KT One；University of South Florida（南佛罗里达大学）；Koç University（科奇大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科技研究基金会基础科学研究所（TBAE））；Tokyo International University（东京国际大学）；Nanoelectronics Research Center（纳米电子学研究中心）
Dicke states are a family of multi-qubit quantum states with interesting entanglement properties and have been observed in many experiments. We construct entanglement witnesses for detecting genuine multiparticle entanglement in the vicinity of these states. We use the approach of PPT mixtures to derive the conditions analytically. For nearly all cases, our criteria are stronger than all conditions previously known.
We propose the analog quantum simulation of generalized Dicke models in trapped ions. By combining bicromatic laser interactions on multiple ions we can generate all regimes of light-matter coupling in these models, where here the light mode is mimicked by a motional mode. We present numerical simulations of the three-qubit Dicke model both in the weak field (WF) regime, where the Jaynes-Cummings behaviour arises, and the ultrastrong coupling (USC) regime, where rotating-wave approximation (RWA) cannot be considered. We also simulate the two-qubit biased Dicke model in the WF and USC regimes a…
We calculate the transmission spectrum of a superconducting circuit realization of the Dicke model and identify spectroscopic features that can serve as signatures of the superradiant phase. In particular, we calculate the resonance frequencies of the system as functions of the bias term, which is usually absent in studies on the Dicke model but is commonly present in superconducting qubit circuits. To avoid over-complicating the proposed circuit, we assume a fixed coupling strength. This situation precludes the possibility of observing signatures of the phase transition by varying the couplin…
The celebrated Majorana representation is exploited to investigate spin squeezing in different classes of pure symmetric states of N qubits with two distinct spinors, namely the Dicke-class of states. On obtaining a general expression for spin squeezing parameter, the variation of squeezing for different configurations is studied in detail.It is shown that the states in the Dicke-class, characterized by two-distinct non-orthogonal spinors, exhibit squeezing.
We present an experimental method to produce 4-qubit phased Dicke states, based on a source of 2-photon hyperentangled states. By introducing quantum noise in the multipartite system in a controlled way, we have tested the robustness of these states. To this purpose the entanglement of the resulting multipartite entangled mixed states has been verified by using a new kind of structural witness.
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…
Deterministic preparation of entangled Dicke states
Institute for Quantum Science and Engineering, Texas A&M University（德州农工大学量子科学与工程研究所）；Department of Biological and Agricultural Engineering, Texas A&M University（德州农工大学生物与农业工程系）
We study effective light-matter interactions in a circuit QED system consisting of a single $LC$ resonator, which is coupled symmetrically to multiple superconducting qubits. Starting from a minimal circuit model, we demonstrate that in addition to the usual collective qubit-photon coupling the resulting Hamiltonian contains direct qubit-qubit interactions, which have a drastic effect on the ground and excited state properties of such circuits in the ultrastrong coupling regime. In contrast to a superradiant phase transition expected from the standard Dicke model, we find an opposite mechanism…
