اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHeisenberg Uncertainty Principle as Probe of Entanglement Entropy: Application to Superradiant Quantum Phase Transitions
249
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy and one of the most fundamental and simplest measure of the quantum fluctuations, the Heisenberg uncertainty principle. Then, we show that the latter represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian, which embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamic limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $Delta xDelta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two level systems. Our findings, which show that the entanglement properties between light and matter can be accessed through the Heisenberg uncertainty principle, can be tested using Bose-Einstein condensates in optical cavities and circuit quantum electrodynamics
قيم البحث
اقرأ أيضاً
Although the oscillator strength sum rule forbids the phase transition in ideal non-interacting two-level atoms systems, we present the possibility of the quantum phase transition in the coupled two-level atoms in a cavity. The system undergoes the s
uperradiant phase transition in the thermodynamics limit and this transition is account for the atom-atom attractive interaction, exhibiting a violation of the sum rule. The bosonic coherent state technique has been adopted to locate the quantum critical point accurately in the finite-size system. We predict the existence of the superadiant phase transition as the number of atoms increases, satisfying all the constraints imposed by the sum rule.
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence
of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.
We prove, by means of a unified treatment, that the superradiant phase transitions of Dicke and classical oscillator limits of simple light-matter models are indeed of the same type. We show that the mean-field approximation is exact in both cases, a
nd compute the structure and location of the transitions in parameter space. We extend this study to a fuller range of models, paying special attention to symmetry considerations. We uncover general features of the phase structure in the space of parameters of these models.
We show that entanglement monotones can characterize the pronounced enhancement of entanglement at a quantum phase transition if they are sensitive to long-range high order correlations. These monotones are found to develop a sharp peak at the critic
al point and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlations and verify that these experimentally accessible quantities indeed encode entanglement information and probe separability.
We study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-$S$ truncation, where there is an infinite-o
rder Gaussian (IOG) transition for $S = 1$ and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for $S ge 2$. We show that the height of the peak in the fidelity susceptibility ($chi_F$) converges to a finite thermodynamic value as a power law of $1/L$ for the IOG transition and as $1/ln(L)$ for BKT transitions. The peak position of $chi_F$ resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant ($S^{prime}_{vN}$) has a peak height that diverges as $ln^{2}(L)$ [$ln^{3}(L)$] for $S = 1$ ($S ge 2$) and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and crosscheck the results with the value of the central charge $c = 1$. The crossing point of $chi_F$ between different system sizes is at the IOG point for $S = 1$ but is inside the gapped phase for $S ge 2$, while those of $S^{prime}_{vN}$ are at the phase-transition points for all $S$ truncations. Our work elaborates how to use the finite-size scaling of $chi_F$ or $S^{prime}_{vN}$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
