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arXiv:1807.04617 · Optics Express

Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions

Li-Ping Yang, Zubin Jacob

Published Apr 1, 2019• 34 citations
arXivHTMLPDF

Abstract

) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.

DOI
10.1364/oe.27.010482

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) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.
We introduce a first-order quantum-phase-transition model, which exhibits giant sensitivity χ∝N2 at the critical point. Exploiting this effect, we propose a quantum critical detector (QCD) to amplify weak input signals. The time-dynamic QCD functions by triggering a first-order dynamical quantum phase transition in a system of spins with long-range interactions coupled to a bosonic mode. We numerically demonstrate features of the dynamical quantum phase transition, which leads to a time-dependent quantum gain. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio of this QCD. Our QCD can be a resource for metrology, weak signal amplification, and single photon detection.
The quantum critical detector (QCD), recently introduced for weak signal amplification [L.-P. Yang and Z. Jacob, Opt. Express 27, 10482 (2019)], functions by exploiting high sensitivity near the phase transition point of first-order quantum phase transitions (QPTs). We contrast the behavior of the first-order and the second-order quantum phase transitions in the detector. We find that the giant sensitivity, which can be utilized for quantum amplification, only exists in the first-order QPTs. We define two new magnetic order parameters to quantitatively characterize the first-order QPT of the interacting spins in the detector. We also introduce the Husimi Q-functions as a powerful tool to show the fundamental change in the ground-state wave function of the detector during the QPTs, especially the intrinsic dynamical change within the detector during a quantum critical amplification. We explicitly show the high figures of merit of the QCD via the quantum gain and the signal-to-quantum noise ratio. Specifically, we predict the existence of a universal first-order QPT in the interacting-spin system resulting from two competing ferromagnetic orders. Our results motivate new designs of weak signal detectors by engineering first-order QPTs, which are of fundamental significance in the search for new particles, quantum metrology, and information science.
The temporal dynamics of large quantum systems perturbed weakly by a single excitation can give rise to unique phenomena at the quantum phase boundaries. Here, we develop a time-dependent model to study the temporal dynamics of a single photon interacting with a defect within a large system of interacting spins. Our model can lead to a single-photon detector if the system of spins is engineered to simulate a first-order quantum phase transition (QPT). We show that the absorption of a single photon pulse by an engineered defect (i.e., a nitrogen-vacancy center) can nucleate a single shot quantum measurement. This concept of a single-shot detection event (click) is different from parameter estimation which requires repeated measurements. The crucial step of amplifying the weak quantum signal occurs by coupling the defect to a system of interacting spins biased close to a QPT point. The macroscopic spin-order change during the QPT generates an amplified signal, which can be read out by a classical device. Our work paves the way for studying the temporal dynamics of large quantum systems interacting with a single photon.
Phase transitions have recently been formulated in the time domain of quantum many-body systems, a phenomenon dubbed dynamical quantum phase transitions (DPTs), whose phenomenology is often divided in two types. One refers to distinct phases according to long-time averaged order parameters, while the other is focused on the nonanalytical behavior emerging in the rate function of the Loschmidt echo. Here we show that such DPTs can be found in systems with few degrees of freedom; i.e., they can take place without resorting to the traditional thermodynamic limit. We illustrate this by showing the existence of the two types of DPTs in a quantum Rabi model---a system involving a spin-12\frac{1}{2}21​ and a bosonic mode. The dynamical criticality appears in the limit of an infinitely large ratio of the spin frequency with respect to the bosonic one. We determine its dynamical phase diagram and study the long-time averaged order parameters, whose semiclassical approximation yields a jump at the transition point. We find the critical times at which the rate function becomes nonanalytical, showing its associated critical exponent as well as the corrections introduced by a finite frequency ratio. Our results open the door for the study of DPTs without the need to scale up the number of components, thus allowing for their investigation in well controllable systems.
Abstract Symmetry-breaking quantum phase transitions lead to the production of topological defects or domain walls in a wide range of physical systems. In second-order transitions, these exhibit universal scaling laws described by the Kibble–Zurek mechanism, but for first-order transitions a similarly universal approach is still lacking. Here, we propose a spinor Bose–Einstein condensate as a testbed system where critical scaling behaviour in a first-order quantum phase transition can be understood from generic properties. We demonstrate the applicability of the Kibble–Zurek mechanism for this transition to determine the critical exponents for: (1) the onset of the decay of the metastable state on short times scales, and (2) the number of resulting phase-separated ferromagnetic domains at longer times, as a one-dimensional spin-1 condensate is ramped across a first-order quantum phase transition. The predictions are in excellent agreement with mean-field numerical simulations and provide a paradigm for studying the decay of metastable states in experimentally accessible systems.
We study the quantum speed limit time (QSLT) of a coupled system consisting of a central spin and its surrounding environment, and the environment is described by a general XY spin-chain model. For initial pure state, we find that the local anomalous enhancement of the QSLT occurs near the critical point. In addition, we investigate the QSLT for arbitrary time-evolution state in the whole dynamics process and find that the QSLT will decay monotonously and rapidly at a large size of environment near the quantum critical point. These anomalous behaviors in the critical vicinity of XY spin-chain environment can be used to indicate the quantum phase transition point. Especially for the XX spin-chain environment, we find that the QSLT displays a sudden transition from discontinuous segmented values to a steady value at the critical point. In this case, the non-Makovianity and the Loschmidt echo are incapable of signaling the critical value of the transverse field, while the QSLT can still witness the quantum phase transition. So, the QSLT provides a further insight and sharper identification of quantum criticality.