Dicke States Research Articles

In-phase collective unconventional photon blockade and its stability in asymmetrical cavity containing N bosonic atoms

Abstract We present a work of cavity-driven QED system combined an asymmetrical Fabry-Perot cavity and N two-level atoms (TLAs) and show the convenience of simplifying from distinguishable atoms to undistinguishable bosons when atoms are prepared in the same initial state. Such simplification is valid even when the atoms are not prepared in the in-phase condition, since any partial in-phase initial state will evolve into the ground state through a relaxation process. Thus, we get a reduced group of differential equations by introducing the Dicke states, and the under-zero Lyapunov exponents verify its stability. We also work out the collective unconventional photon blockade (UCPB) and get two kinds of giant nonreciprocal UCPBs (NUCPBs) in the weak-driving approximation. Results show that we can employ N non-interacting bosonic atoms to generate a collective UCPB instead of a monoatomic UCPB as UCPB conditions do not vary with the number of atoms. Furthermore, the forward giant NUCPB only occurring for N larger than a certain number, as well as the backward giant NUCPB, are controllable by the cavity asymmetry and by the number of atoms. Our findings suggest a prospective approach to the generation of quantum nonreciprocity by N identical atoms.

Unmasking the polygamous nature of quantum nonlocality

Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality, then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signaling principle, and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here, we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements, and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of [Formula: see text] observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.

Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States.

Quantum entanglement is a fundamental characteristic of quantum mechanics, and understanding the robustness of entanglement across different mixed states is crucial for comprehending the entanglement properties of general quantum states. In this paper, the robustness of entanglement of Dicke-W and Greenberger-Horne-Zeilinger (GHZ) mixed states under different mixing ratios is calculated using the entanglement witness method. The robustnesses of entanglement of Dicke-W and GHZ mixed states are different when the probability ratio of Dicke to W is greater than 32 and less than 32. For the probability of Dicke and W states greater than or equal to 32, we study the robustness of entanglement of Dicke and GHZ mixed states and analyze and calculate their upper and lower bounds. For the probability of Dicke and W states less than 32, we take the equal probability ratio of Dicke and W states as an example and calculate and analyze the upper and lower bounds of their robustness of entanglement in detail.

Entanglement in selected binary tree states: Dicke or total spin states or particle-number-projected BCS states

Entanglement in selected binary tree states: Dicke or total spin states or particle-number-projected BCS states

Spin‐s$s$ Dicke States and Their Preparation

AbstractThe notion of spin‐ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits.

Role of polaron dressing in superradiant emission dynamics

Cooperative effects of multiple quantum emitters are characterized by transitions via delocalized collective states with altered emission properties due to the existence of interemitter coherences. When realized with excitonic condensed-matter nanostructures, these effects are significantly affected by the presence of strong emitter-phonon coupling, which leads to the formation of polarons. We show that, while for single-emitter emission into free space this formation has no impact on its radiative lifetime, the same is not true for superradiant emission. Considering the case of two indistinguishable quantum emitters, we analyze how polaron dressing affects collective photon emission by mixing bright and dark Dicke states. Our numerical simulations show that this mixing crucially depends on the circumstances of the excitation of the system: Depending on the pulse length of an exciting laser, one can choose to either prepare polaronic Dicke states, or bare electronic Dicke states, changing the superradiant decay characteristics of the system. Additionally, we derive analytic expressions for these limiting cases, which match the results of numerically exact calculations. Published by the American Physical Society 2024

Cooperative Decay of an Ensemble of Atoms in a One-Dimensional Chain with a Single Excitation

We propose a new expression of the cooperative decay rate of a one-dimensional chain of N two-level atoms in the single-excitation configuration. From it, the interference nature of superradiance and subradiance arises naturally, without the need to solve the eigenvalue problem of the atom–atom interaction Green function. The cooperative decay rate can be interpreted as the imaginary part of the expectation value of the effective non-Hermitian Hamiltonian of the system, evaluated over a generalized Dicke state of N atoms in the single-excitation manifold. Whereas the subradiant decay rate is zero for an infinite chain, it decreases as 1/N for a finite chain. A simple approximated expression for the cooperative decay rate is obtained as a function of the lattice constant d and the atomic number N. The results are obtained first for the scalar model and then extended to the vectorial light model, assuming all the dipoles aligned.

Two-dimensional and absolutely entanglement-breaking subspaces

Entanglement-breaking (EB) subspaces determine the additivity of entanglement of formation (EOF), which is a long-standing issue in quantum information. We explicitly construct the two-dimensional EB subspaces of any bipartite system, when system dimensions are equal, and we apply the subspaces to construct EB spaces of arbitrary dimensions. We also present partial construction when system dimensions are different. Then, we present the notion and properties of EB subspaces for some systems, and in particular the absolute EB subspaces. We construct some examples of absolute EB subspaces, as well as EB subspaces for some systems by using multiqubit Dicke states.

Fast preparation of Dicke state by shortcuts to adiabatic passages

Dicke state is one of the most useful multipartite quantum states. In this paper, by utilizing the method of designing the evolution operators to construct shortcuts to adiabatic passages (STAP), we have implemented the fast preparation of Dicke states |D3(2)〉 and |D4(2)〉 with one step. Specifically, with the assistance of quantum Zeno dynamics, the original Hamiltonian of the system is simplified into an effective Hamiltonian. Under the dynamic evolution of this effective Hamiltonian, the pulse control is realized by selecting two appropriate auxiliary parameters. This not only greatly shortens the evolution time but also optimizes the operation of the quantum system. In addition, we have discussed the effects of decoherence, parameter fluctuations and noise on fidelity. The results indicate that the proposed protocol maintains high fidelity. Finally, the fast preparation of Dicke state |Dn(2)〉 can be achieved based on the same method.

Achieving the Heisenberg limit with Dicke states in noisy quantum metrology

Achieving the Heisenberg limit with Dicke states in noisy quantum metrology

Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory

Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph algebras and Brauer configuration algebras to investigate the algebras of tame and wild representation types. An appropriated system of multisets (called a Brauer configuration) induces these algebras via a suitable bounded quiver (or bounded directed graph), and the combinatorial properties of such multisets describe corresponding indecomposable projective modules, the dimensions of the algebras and their centers. Undirected graphs are examples of Brauer configuration messages, and the description of the related data for their induced Brauer configuration algebras is said to be the Brauer analysis of the graph. This paper gives closed formulas for the dimensions of Brauer configuration algebras (and their centers) induced by Cayley and nilpotent graphs defined by some finite groups and finite commutative rings. These procedures allow us to give examples of Hamiltonian digraph constructions based on Cayley graphs. As an application, some quantum entangled states (e.g., Greenberger–Horne–Zeilinger and Dicke states) are described and analyzed as suitable Brauer messages.

Dicke State Generation and Extreme Spin Squeezing via Rapid Adiabatic Passage.

Considering the unique energy level structure of the one-axis twisting Hamiltonian in combination with standard rotations, we propose the implementation of a rapid adiabatic passage scheme on the Dicke state basis. The method permits to drive Dicke states of the many-atom system into entangled states with maximum quantum Fisher information. The designed states allow us to overcome the classical limit of phase sensitivity in quantum metrology and sensing. We show how to generate superpositions of Dicke states, which maximize metrological gain for a Ramsey interferometric measurement. The proposed scheme is remarkably robust to variations of the driving field and has favorable time scaling, especially for a small to moderate (∼1000) number of atoms, where the total time does not depend on the number of atoms.

Globally optimal interferometry with lossy twin Fock probes

Parity or quadratic spin (e.g., Jz2) readouts of a Mach–Zehnder (MZ) interferometer probed with a twin Fock (TF) input state allow saturating the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles but only when the interferometer phase θ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at θ = 0, whereas better-than-standard quantum limit performance of the Jz2 readout is restricted to an o(N) occupation imbalance. We show that a method of moments readout of two quadratic spin observables Jz2 and J+2+J−2 is globally optimal for Dicke state probes; i.e., the error saturates the QFI for all θ. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on TF states, showing that the method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of θ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four-mode state |N4,N4,N4,N4〉 and its lossy counterparts, showing that an advantage for the estimation of any linear function of the local MZ phases θ1 and θ2 (compared to independent probing of the MZ phases by two copies of |N4,N4〉) appears when more than one particle is lost.

Production and protection of entanglement via vacuum induced coherences

The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.

Qudit Dicke state preparation

Qudit Dicke states are higher-dimensional analogues of an important class of highly-entangled completely symmetric quantum states known as (qubit) Dicke states. A circuit for preparing arbitrary qudit Dicke states deterministically is formulated. An explicit decomposition of the circuit in terms of elementary gates is presented, and is implemented in cirq for the qubit and qutrit cases.

Clifford orbits from cayley graph quotients

We describe the structure of the $n$-qubit Clifford group $\mathcal{C}_n$ via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we introduce a quotient procedure. Quotienting the Cayley graph by the stabilizer subgroup of a state gives a reduced graph which depicts the state's Clifford orbit. Using this protocol for $\mathcal{C}_2$, we reproduce and generalize the reachability graphs introduced in \cite{Keeler2022}. Since the procedure is state-independent, we extend our study to non-stabilizer states, including the W and Dicke states. Our new construction provides a more precise understanding of state evolution under Clifford circuit action.

Q-analog qudit Dicke states

Dicke states are completely symmetric states of multiple qubits (2-level systems), and qudit Dicke states are their d-level generalization. We define here q-deformed qudit Dicke states using the quantum algebra suq(d) . We show that these states can be compactly expressed as a weighted sum over permutations with q-factors involving the so-called inversion number, an important permutation statistic in Combinatorics. We use this result to compute the bipartite entanglement entropy of these states. We also discuss the preparation of these states on a quantum computer, and show that introducing a q-dependence does not change the circuit gate count.

Entangling two Dicke states in a periodic modulated quantum system

Entangling two Dicke states in a periodic modulated quantum system

Following Forrelation – quantum algorithms in exploring Boolean functions' spectra

<p style='text-indent:20px;'>Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al., 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation spectrum, and the autocorrelation spectrum. We introduce the existing 2-fold Forrelation formulation with bent duality-based promise problems as desirable instantiations. Next, we concentrate on the 3-fold version through two approaches. First, we judiciously set up some of the functions in 3-fold Forrelation so that given oracle access, one can sample from the Walsh Spectrum of <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula>. Using this, we obtain improved results than what one can achieve by exploiting the Deutsch-Jozsa algorithm. In turn, it has implications in resiliency checking. Furthermore, we use a similar idea to obtain a technique in estimating the cross-correlation (and thus autocorrelation) value at any point, improving upon the existing algorithms. Finally, we tweak the quantum algorithm with the superposition of linear functions to obtain a cross-correlation sampling technique. This is the first cross-correlation sampling algorithm with constant query complexity to the best of our knowledge. This also provides a strategy to check if two functions are uncorrelated of degree <inline-formula><tex-math id="M2">\begin{document}$ m $\end{document}</tex-math></inline-formula>. We further modify this using Dicke states so that the time complexity reduces, particularly for constant values of <inline-formula><tex-math id="M3">\begin{document}$ m $\end{document}</tex-math></inline-formula>.</p>

Tuning perovskite nanocrystal superlattices for superradiance in the presence of disorder.

The cooperative emission of interacting nanocrystals is an exciting topic fueled by recent reports of superfluorescence and superradiance in assemblies of perovskite nanocubes. Several studies estimated that coherent coupling is localized to a small fraction of nanocrystals (10-7-10-3) within the assembly, raising questions about the origins of localization and ways to overcome it. In this work, we examine single-excitation superradiance by calculating radiative decays and the distribution of superradiant wave function in two-dimensional CsPbBr3 nanocube superlattices. The calculations reveal that the energy disorder caused by size distribution and large interparticle separations reduces radiative coupling and leads to the excitation localization, with the energy disorder being the dominant factor. The single-excitation model clearly predicts that, in the pursuit of cooperative effects, having identical nanocubes in the superlattice is more important than achieving a perfect spatial order. The monolayers of large CsPbBr3 nanocubes (LNC = 10-20nm) are proposed as model systems for experimental tests of superradiance under conditions of non-negligible size dispersion, while small nanocubes (LNC = 5-10nm) are preferred for realizing the Dicke state under ideal conditions.