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arXiv:1905.07420 · Journal of Applied Physics

Engineering first-order quantum phase transitions for weak signal detection

Li-Ping Yang, Zubin Jacob

Published Nov 6, 2019• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.5121558

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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.
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.
) 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.
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.
Abstract Investigations into first-order quantum phase transition (QPT) remain unclear in comparison to those of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and, at the same time, the concepts of universality class and critical scaling can be characterized by critical exponents. Here, we present a comparison study of these two kinds of QPT in the transverse Ising model; the emphasis is on the first-order QPT. In the absence of a longitudinal field, the ground state of the model exhibits a second-order QPT from the paramagnetic phase to the ferromagnetic phase, which is smeared out once the longitudinal field is applied. Surprisingly, the first excited state involves a first-order QPT as the longitudinal field increases, which has not been reported in the literature. Within the framework of the pattern picture, we clearly identify the difference between these two kinds of QPT: for the continuous QPT, only the pattern flavoring the ferromagnetic phase is always dominant over the others. By contrast, there are at least two competitive patterns in the first-order QPT, which is further indicated by the patterns’ occupancies, calculated by pattern projections on the ground- and first excited-state wavefunctions. Our results not only have a fundamental significance in the understanding of the nature of QPTs, but also a practical interest in quantum simulations used to test the present findings.
Aim and Scope of this Book A plethora of systems exhibit phase transitions as the temperature or some other parameter is changed. Examples range from the ice-water phase transition observed in our daily life to the loss of ferromagnetism in iron or to the more sophisticated Mott insulator-superfluid phase transition observed in optical lattices [343]. The last five decades have witnessed a tremendous upsurge in the studies of phase transitions at finite temperature [727, 149, 333, 136, 494, 541, 556]. The success of Landau-Ginzburg theories and the concepts of spontaneous symmetry breaking and the renormalization group [27, 410, 821, 578] in explaining many of the finite temperature phase transitions occurring in nature has been spectacular. In this book, we will consider only a subclass of phase transitions called quantum phase transitions (QPTs) [154, 658, 725, 799, 185, 63, 62, 66, 141, 744] and we will discuss these mainly from the view point of recent studies of information and dynamics. QPTs are zero temperature phase transitions which are driven by quantum fluctuations and are usually associated with a non-analyticity in the ground state energy density of a quantum many-body Hamiltonian. We will focus on continuous QPTs where the order parameter vanishes continuously at the quantum critical point (QCP) at some value of the parameters which characterize the Hamiltonian. We will not discuss first order quantum phase transitions associated with an abrupt change in the order parameter. Usually, a first order phase transition is characterized by a finite discontinuity in the first derivative of the ground state energy density. A continuous QPT is similarly characterized by a finite discontinuity, or divergence, in the second derivative of the ground state energy density, assuming that the first derivative is continuous. This is of course the classical definition; we will later mention some QPTs where the ground state energy density is not necessarily singular.
Discontinuous quantum phase transitions besides their general interest are clearly relevant to the study of heavy fermions and magnetic transition metal compounds. Recent results show that in many systems belonging to these classes of materials the magnetic transition changes from second order to first order as they approach the quantum critical point (QCP). We investigate here some mechanisms that may be responsible for this change, specifically the coupling of the order parameter to soft modes and the competition between different types of order near the QCP. For weak first order quantum phase transitions general results are obtained. In particular, we describe the thermodynamic behaviour at this transition when it is approached from finite temperatures. This is the discontinuous equivalent of the non-Fermi-liquid trajectory close to a conventional QCP in a heavy-fermion material.