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arXiv:2302.11513 · Physical Review A

Hybrid nonlocality via atom-photon interactions with and without impurities

Pritam Halder, Ratul Banerjee, Saptarshi Roy, Aditi Sen

Published Jan 21, 2025• 4 citations
arXivHTMLPDF

Abstract

To obtain Bell statistics from hybrid systems composed of finite- and infinite-dimensional systems, we propose a hybrid measurement scheme, in which the continuous mode is measured using the generalized pseudospin operators, while the finite (two)-dimensional system is measured in the usual Pauli basis. Maximizing the Bell expression with these hybrid measurement settings leads to the violations of local realism in the hybrid system, which is referred to as hybrid nonlocality. We demonstrate the utility of our strategy in a realistic setting of cavity quantum electrodynamics, where an atom interacts resonantly with a single mode of an electromagnetic field under the Jaynes-Cummings Hamiltonian. We dynamically compute the quenched averaged value of hybrid nonlocality in imperfect situations by incorporating disorder in the atom-cavity coupling strength. In the disordered case, we introduce two kinds of measurement scenarios to determine the Bell statistics---in one situation, experimentalists can tune the optimal settings according to the interaction strength, while such controlled power is absent in the other case. In contrast to the oscillatory behavior observed in the ordered case, the quenched averaged violation saturates to a finite value in some parameter regimes in the former case. We also examine the connection between Wigner negativity and hybrid nonlocality.

DOI
10.1103/physreva.111.012431

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To obtain Bell statistics from hybrid systems composed of finite- and infinite-dimensional systems, we propose a hybrid measurement scheme, in which the continuous mode is measured using the generalized pseudospin operators, while the finite (two)-dimensional system is measured in the usual Pauli basis. Maximizing the Bell expression with these hybrid measurement settings leads to the violations of local realism in the hybrid system, which is referred to as hybrid nonlocality. We demonstrate the utility of our strategy in a realistic setting of cavity quantum electrodynamics, where an atom interacts resonantly with a single mode of an electromagnetic field under the Jaynes-Cummings Hamiltonian. We dynamically compute the quenched averaged value of hybrid nonlocality in imperfect situations by incorporating disorder in the atom-cavity coupling strength. In the disordered case, we introduce two kinds of measurement scenarios to determine the Bell statistics---in one situation, experimentalists can tune the optimal settings according to the interaction strength, while such controlled power is absent in the other case. In contrast to the oscillatory behavior observed in the ordered case, the quenched averaged violation saturates to a finite value in some parameter regimes in the former case. We also examine the connection between Wigner negativity and hybrid nonlocality.
We revisit the generation and evolution of Bell nonlocality in hybrid scenarios of which the dynamics is determined by the Jaynes-Cummings Hamiltonian, a relevant example of which is the atom-cavity system. Previous approaches evaluate the nonlocality through the well-known qubit-qubit Clauser-Horne-Shimony-Holt (CHSH) formulas, using combinations of pseudospin operators for the electromagnetic (EM) field observables. While such an approach is sensible, it is far from optimal. In the present work we have used recent results on optimal Bell violation in qubit-qudit systems, showing that the nonlocality is much greater than previously estimated, both with and without noise. In addition, we provide an optimal treatment of noise, ensuring that our results are the best possible within this framework. We illustrate the results using different initial states for the EM field, including squeezed and coherent states. In addition, we study the asymptotic behavior of the entanglement. Remarkably, starting with a generic separable pure coherent state, the asymptotic mixed state is entangled, though it does not violate CHSH inequalities.
Abstract We investigate the violation of nonlocal realism using various entangled continues- and hybrid-variable states under dichotomic observables. In particular, we consider two cases of dichotomic observables (1) described by a pseudospin operator and (2) given in terms of the Wigner representation of the state in phase space, parity measurement and displacement operation. We address the recently proposed operational measure of nonlocality which describes the probability of local-realism violation under randomly sampled observables. We show the usefulness and limitations of the probability of local-realism violation for the detection of nonlocality. A simple procedure to detect such nonlocal correlations for randomly chosen settings with efficiencies of up to 100% is proposed. The practical advantage of applying random measurements that considerably lowers the experimental requirements is mentioned.
We analyze nonclassical correlations between outcomes of measurements conducted on two spatial radiation modes. These correlations cannot be simulated with statistical mixtures of coherent states or, more generally, with non-negative phase-space functions of quantum states and measurements. We argue that nonclassical correlations are naturally related to Bell nonlocality, the former being a more general class of quantum correlations. Indeed, it is known that local realistic as well as noncontextual models correspond to non-negative solutions to a system of linear equations for the joint probability distributions of all observables. We demonstrate that nonclassical correlations correspond to a particular solution to this system, which may have negative values even if local realism is not violated. A modification of Bell inequalities enables us to test such correlations. At the same time, our approach leads to a formulation of Bell inequalities applicable also to continuous variables. The results are illustrated with two-mode squeezed vacuum states and with hybrid entangled states (Schr\"odinger-Cat states), one mode being analyzed by balanced and the other one by unbalanced homodyne detection.
Bell nonclassicality of a single-photon superposition in two modes, often referred to as ``nonlocality of a single photon,'' is one of the most striking nonclassical phenomena discussed in the context of foundations of quantum physics. Here we show how to robustly violate local realism within the weak-field homodyne measurement scheme for any superposition of one photon with vacuum. Our modification of the previously proposed setups involves tunable beam splitters at the measurement stations, and the local oscillator fields significantly varying between the settings, optimally being on or off. As photon-number-resolving measurements are now feasible, we advocate for the use of the Clauser-Horne Bell inequalities for detection events using precisely defined numbers of photons. We find a condition for optimal measurement settings for the maximal violation of the Clauser-Horne inequality with weak-field homodyne detection, which states that the reflectivity of the local beam splitter must be equal to the strength of the local oscillator field. We show that this condition holds not only for the vacuum--one-photon qubit input state, but also for the superposition of a photon pair with vacuum, which suggests its generality as a property of weak-field homodyne detection with photon-number resolution. Our findings suggest a possible path to employ such scenarios in device-independent quantum protocols.
Abstract This work delves into the nonlocal correlation dynamics of the maximum-Bell nonlocality (MBN), uncertainty-induced nonlocality (UIN), and concurrence of two two-level atoms having time-dependent atomic locations within Tavis-Cummings model. By considering a scenario where the pure two qubits resonantly interact with an even coherent cavity field through a two-photon transition, we explore the nonlocal correlation dynamics of both moving and stationary two-atom configurations under varying conditions and coupling parameters. Our findings reveal that the coherent cavity induces the successful generation of nonlocal correlations between atoms in both modes, with moving atoms exhibiting higher and symmetrical nonlocal correlations. Interestingly, dynamical maps showcase distinct behaviors for atoms at rest, exhibiting precocity at higher atom-cavity strengths. Moreover, equal coupling strength results in lower quantum correlations. The UIN measure emerges as the most robust quantum function, showing enhancements with sustained unequal coupling strengths, contrasting with the MBN and concurrence. These insights offer a nuanced understanding of nonlocal correlations in the Tavis-Cummings model, essential for advancing quantum information science and technology.
Abstract We reconsider the all-optical weak homodyne-measurement based experimental schemes aimed at revealing Bell nonclassicality (‘nonlocality’) of a single photon. We focus on the schemes put forward by Tan et al (TWC, 1991) and Hardy (1994). In our previous work we show that the TWC experiment can be described by a local hidden variable model, hence the claimed nonclassicality is apparent. The nonclassicality proof proposed by Hardy remains impeccable. We investigate which feature of the Hardy’s approach is crucial to disclose the nonclassicality. There are consequential differences between TWC and Hardy setups: (i) the initial state of Hardy is a superposition of a single photon excitation with vacuum in one of the input modes of a 50–50 beamsplitter. In the TWC case there is no vacuum component. (ii) In the final measurements of Hardy’s proposal the local settings are specified by the presence or absence of a local oscillator field (on/off). In the TWC case the auxiliary fields are constant, only phases are varied. We show that in Hardy’s setup the violation of local realism occurs due to the varying strength of the local oscillators. Still, one does not need to operate in the fully on/off detection scheme. Thus, the nonclassicality in a Hardy-like setup cannot be attributed to the single-photon state alone. It is a consequence of its interference with the photons from auxiliary local fields. Neither can it be attributed to the joint state of the single photon excitation and the local oscillator modes, as this state is measurement setting dependent. Despite giving spurious violations of local realism, the TWC scheme can serve as an entanglement indicator, for the TWC state. Nevertheless an analogue indicator based on intensity rates rather than just intensities overperforms it.