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arXiv:2401.00111

High--N00N State Generation: N00N State Output of Floquet Engineering

Yusef Maleki

Published Dec 30, 2023• 0 citations
arXivHTMLPDF

Abstract

Here, we review some quantum architectures designed for the engineering of the N00N state, a bipartite maximally entangled state crucial in quantum metrology applications. The fundamental concept underlying these schemes is the transformation of the initial state $|N\rangle \otimes |0\rangle$ to the N00N state $\frac{1}{\sqrt{2}} (|N\rangle \otimes|0\rangle +|0\rangle \otimes|N\rangle)$, where $|N\rangle$ and $|0\rangle$ are the Fock states with $N$ and $0$ excitations. We show that this state can be generated as a superposition of modes of quantum light, a combination of light and motion, or a superposition of two spin ensembles. The approach discussed here can generate mesoscopic and macroscopic entangled states, such as entangled coherent and squeezed states, as well. We show that a large class of maximally entangled states can be achieved in such an architecture. The extension of these state engineering methods to the multi-mode setting is also discussed.

DOI
10.48550/arxiv.2401.00111

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Here, we review some quantum architectures designed for the engineering of the N00N state, a bipartite maximally entangled state crucial in quantum metrology applications. The fundamental concept underlying these schemes is the transformation of the initial state ∣N⟩⊗∣0⟩|N\rangle \otimes |0\rangle∣N⟩⊗∣0⟩ to the N00N state 12(∣N⟩⊗∣0⟩+∣0⟩⊗∣N⟩)\frac{1}{\sqrt{2}} (|N\rangle \otimes|0\rangle +|0\rangle \otimes|N\rangle)2​1​(∣N⟩⊗∣0⟩+∣0⟩⊗∣N⟩), where ∣N⟩|N\rangle∣N⟩ and ∣0⟩|0\rangle∣0⟩ are the Fock states with NNN and 000 excitations. We show that this state can be generated as a superposition of modes of quantum light, a combination of light and motion, or a superposition of two spin ensembles. The approach discussed here can generate mesoscopic and macroscopic entangled states, such as entangled coherent and squeezed states, as well. We show that a large class of maximally entangled states can be achieved in such an architecture. The extension of these state engineering methods to the multi-mode setting is also discussed.
We review quantum architectures for engineering the N00N state, a bipartite maximally entangled state essential in quantum metrology. These schemes transform the initial state |N⟩⊗|0⟩ into the N00N state, 12(|N⟩⊗|0⟩+|0⟩⊗|N⟩), where |N⟩ and |0⟩ are Fock states with N and 0 excitations, respectively. We demonstrate that this state can be generated through superpositions of quantum light modes, hybrid light–matter interactions, or spin ensembles. Our approach also enables the creation of mesoscopic and macroscopic entangled states, including entangled coherent and squeezed states. Furthermore, we show that a broad class of maximally entangled states can be realized within this framework. Extensions to multi-mode state engineering are also explored.
Quantum entanglement is central to many quantum technologies and is an indispensable ingredient of quantum information theory. These facts make the generation, characterization and quantification of entangled states unavoidable tasks, beside all their fundamental significance. As a particular example of such applications one may consider quantum metrology in which quantum entanglement is shown to have a significant role for beating the classical limits. However, generation, characterization and quantification of suitable entangled states are challenging tasks, in general.\n\nIn this dissertation, we introduce new platforms for engineering multipartite entangled states that are shown to be useful for quantum information processing and quantum metrology applications. In particular, we introduce new methods which can be used for generating N00N states, as one of the most challenging states to generate, enabling realization of such states in both photonic and spintronic architectures. We sketch a rather generic quantum circuit, for the N00N state generation, that could be realized in various quantum systems. Furthermore, we extend the platform for the generation of states beyond the N00N state. Typical examples of such sates could be entangled coherent or squeezed states, for instance, that of specific importance for quantum information and metrology applications. Furthermore, we extend the protocol for the multipartite state scenario. Also, we demonstrate that attaining the ultimate sensitivity in phase estimation is not an exclusive property of the N00N states. As a result, we find a large class of entangled states that could provide us with the ultimate sensitivity achieved by the N00N state.\n\nAs a part of our effort for the N00N state generation, we develop a new scheme where N00N states could be realized in two ensembles of nitrogen--vacancy (NV) centers in diamond. This could be interesting by noting the fact that NV centers in diamonds provide a remarkably long coherence time, even at the room temperature. This opens up new possibilities for protecting N00N states against decoherence.\n\nMoreover, having the long coherence time of the ensembles of the NV centers, we show that a hybrid quantum system consisting of three ensembles of NV centers coupled to a superconducting device enables the generation of controllable macroscopic multipartite entangled states, which could be used as a building block for quantum networks.\n\nFurthermore, we investigate entanglement of nonorthogonal states in details, and more specifically, we obtain a closed-form analytical expression for the entanglement degree of a multipartite qutrit state, that offers a quantitative measure for entanglement nnn-mode nonorthogonal qutrit states with an arbitrary nnn. Such higher dimensional entangled states could be useful in quantum communication protocols.\n\n Finally, we introduce a new configuration where any pair of quantum states can perfectly be swapped between two quantum resonators enabling a realization of a universal swap operation in photonics systems. This can serve as a building block of various quantum information processors.
Quantum states of light, such as squeezed states or entangled states, can be used to make measurements (metrology), produce images, and sense objects with a precision that far exceeds what is possible classically, and also exceeds what was once thought to be possible quantum mechanically. The primary idea is to exploit quantum effects to beat the shot-noise limit in metrology and the Rayleigh diffraction limit in imaging and sensing. Quantum optical metrology has received a boost in recent years with an influx of ideas from the rapidly evolving field of optical quantum information processing. Both areas of research exploit the creation and manipulation of quantum-entangled states of light. We will review some of the recent theoretical and experimental advances in this exciting new field of quantum optical metrology, focusing on examples that exploit a particular two-mode entangled photon state – the High-N00N state.
We show how an idealized measurement procedure can condense photons from two modes into one and how, by feeding forward the results of the measurement, it is possible to generate efficiently superposition states commonly called N00N states. For the basic procedure sources of number states leak onto a beam splitter, and the output ports are monitored by photodetectors. We find that detecting a fixed fraction of the input at one output port suffices to direct the remainder to the same port, with high probability, however large the initial state. When instead photons are detected at both ports, macroscopic quantum superposition states are produced. We describe a linear-optical circuit for making the components of such a state orthogonal, and another to convert the output to a N00N state. Our approach scales exponentially better than existing proposals. Important applications include quantum imaging and metrology.
An ensemble of nitrogen-vacancy (NV) centers coupled to a circuit QED device is shown to enable an efficient, high-fidelity generation of high-N00N states. Instead of first creating entanglement and then increasing the number of entangled particles NNN, our source of high-N00N states first prepares a high-NNN Fock state in one of the NV ensembles and then entangles it to the rest of the system. With such a strategy, high-NNN N00N states can be generated in just a few operational steps with an extraordinary fidelity. Once prepared, such a state can be stored over a longer period of time due to the remarkably long coherence time of NV centers.
This dissertation presents theoretical and computational investigations into non-equilibrium quantum dynamics in engineered systems, with a central focus on entanglement generation for quantum metrology. The primary contributions establish the scalable and robust generation of entanglement in the form of two-mode squeezing in bilayers of power-law interacting quantum spins and uncover a novel dynamical phase transition. We develop a Floquet protocol utilizing spatio-temporal control to engineer spin-spin interactions tailored to the initial state and desired entanglement dynamics, thereby improving the standard quantum limit of 1/√N scaling of the sensitivity in system size N to approach the ultimate Heisenberg limit of 1/N. For a wide range of power-law interactions (1/rα), this approach creates exponentially fast entangled pairs of excitations between the layers. We then reveal a dynamical phase transition in the two-mode squeezing dynamics by identifying universal scaling in terms of system parameters and a divergent time-scale. We establish two distinct phases: a fully collective phase exhibiting Heisenberg-limited squeezing and a partially collective phase with scalable but sub-Heisenberg squeezing. A full set of critical exponents is derived, and a universal scaling collapse of the dynamics is demonstrated, framing entanglement generation within the theory of non-equilibrium critical phenomena. We also apply advanced computational methods to other quantum and classical engineered systems. We investigate quantum transport that maps conductivity to the disorder-driven phase diagram of two-dimensional Dirac fermions. We also design a high-efficiency, lead-free tandem photovoltaic cell. Collectively, this research provides a framework for harnessing quantum control to probe and enhance functionality in complex systems, from fundamental quantum sensing to applied materials design.