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arXiv:1906.01858 · Physical Review A

Quantum metrology enhanced by coherence-induced driving in a cavity-QED setup

Weijun Cheng, S. C. Hou, Zhihai Wang, X. X. Yi

Published Nov 12, 2019• 16 citations
arXivHTMLPDF

Abstract

We propose a quantum metrology scheme in a cavity QED setup to achieve the Heisenberg limit. In our scheme, a series of identical two-level atoms randomly pass through and interact with a dissipative single-mode cavity. Different from the entanglement-based Heisenberg limit metrology scheme, we do not need to prepare the atomic entangled states before they enter into the cavity. We show that the initial atomic coherence will induce an effective driving to the cavity field, whose steady state is an incoherent superposition of orthogonal states, with the superposition probabilities being dependent on the atom-cavity coupling strength. By measuring the average photon number of the cavity in the steady state, we demonstrate that the root mean square of the fluctuation of the atom-cavity coupling strength is proportional to $1/{N}_{c}^{2}$ (${N}_{c}$ is the effective atom number interacting with the photon in the cavity during its lifetime). It implies that we have achieved the Heisenberg limit in our quantum metrology process. We also discuss the experimental feasibility of our theoretical proposal. Our findings may find potential applications in quantum metrology technology.

DOI
10.1103/physreva.100.053825

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In this paper, we consider the application of quantum reservoir engineering in quantum metrology. More precisely, we are concerned with a system setup where a sequence of atoms constructing the “time-varying” quantum reservoir interact, in turn, with the trapped field in a cavity through the Jaynes–Cummings Hamiltonian. In particular, we were able to manipulate the initial states of reservoir atoms in order to enhance estimation precision regarding the coupling strength between each atom and the cavity (the coupling strength between each atom and the cavity was assumed to be identical). The novelty of this work lies in alternately preparing the atoms at two different states in a pairwise manner, such that the cavity could converge into a squeezed state with photonic loss to the environment taken into account. The control scheme proposed here thus leads to higher precision compared to the previous work where reservoir atoms were initialized at the same state, which drove the cavity to a coherent state. Detailed theoretical analysis and numerical simulations are also provided. In addition, this system setup and the associated control scheme are easily implemented for quantum metrology, since no entanglement is required for the preparation of atom states, and the final cavity state can stay steady.
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We propose a probabilistic scheme to prepare a maximally entangled state between a pair of two-level atoms coupled to a leaking cavity mode in circuit QED, without requiring precise time control of the system evolution and initial atomic state. We show that the steady state of this dissipative system is a mixture of two parts, where the atoms are either in their ground state or in a maximally entangled one. Then, by applying a weak probe field to the cavity mode, we are able to discriminate those states without disturbing the atomic system, i.e., to perform a quantum nondemolition measurement via the cavity transmission. In this scheme, one has maximum cavity transmission only when the atomic system is in an entangled state, so that a single click in the detector is enough to be sure that the atoms are in a maximally entangled state. Our scheme relies on an interference effect as it happens in an electromagnetically induced transparency phenomenon so that it works even in the limit of a cavity decay rate much stronger than the atom-field coupling.
We propose a scheme to generate superposition and entanglement between the mesoscopic squeezed vacuum states by considering the two-photon interaction of NNN two-level atoms in a cavity with high quality factor, assisted by a strong driving field. By virtue of specific choices of the cavity detuning, a number of multiparty entangled states can be prepared, including the entanglement between the atomic and the squeezed vacuum cavity states and between the squeezed vacuum states and the coherent states of the cavities. We also present how to prepare entangled states and ``Schr\"odinger cats'' states regarding the squeezed vacuum states of the cavity modes. The possible extension and application of our scheme are discussed. Our scheme is close to the reach with current cavity QED techniques.
Engineering atom-atom interactions is essential both for controlling novel phases of matter and for efficient preparation of many-body entangled states, which are key resources in quantum communication, computation, and metrology. In this work, we propose a scheme to tailor these interactions by coupling driven atom pairs to optical cavity photons via a molecular state in the dispersive regime, resulting in an effective photon-field-dependent potential. As an illustrative example, by analyzing the quantum Fisher information, we show that such induced interactions can generate robust many-body entanglement in two-mode ultracold bosons in an optical cavity. By tuning the photon-induced interactions through the cavity drive, we identify conditions for preparing highly entangled states on timescales that mitigate decoherence due to photon loss. Our results show that entanglement formation rate scales strongly with both photon and atom number, dramatically reducing the timescale compared to bare atomic interactions. We also identify an optimal measurement for exploiting the metrological potential of the atomic state in an interferometric protocol with significant photon losses, saturating the quantum Cramer-Rao lower bound. Furthermore, we show that despite these losses the atomic state exhibits strong Bell correlations. Our results pave the way for engineering atom-atom interactions to study novel phases of light and matter in hybrid atom-photon systems, as well as for tailoring complex quantum states for new quantum technology protocols and fundamental tests of quantum mechanics.