ترغب بنشر مسار تعليمي؟ اضغط هنا

Simulating broken $cal PT$-symmetric Hamiltonian systems by weak measurement

106   0   0.0 ( 0 )
 نشر من قبل Ray-Kuang Lee
 تاريخ النشر 2018
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

By embedding a $cal PT$-symmetric (pseudo-Hermitian) system into a large Hermitian one, we disclose the relations between $cal{PT}$-symmetric Hamiltonians and weak measurement theory. We show that the amplification effect in weak measurement on a conventional quantum system can be used to effectively simulate a local broken $cal PT$-symmetric Hamiltonian system, with the pre-selected state in the $cal PT$-symmetric Hamiltonian system and its post-selected state resident in the dilated Hamiltonian system.



قيم البحث

اقرأ أيضاً

We theoretically study the dynamics of typical optomechanical systems, consisting of a passive optical mode and an active mechanical mode, in the $mathcal{PT}$- and broken-$mathcal{PT}$-symmetric regimes. By fully analytical treatments for the dynami cs of the average displacement and particle numbers, we reveal the phase diagram under different conditions and the various regimes of both $mathcal{PT}$-symmetry and stability of the system. We find that by appropriately tuning either mechanical gain or optomechanical coupling, both phase transitions of the $mathcal{PT}$-symmetry and stability of the system can be flexibly controlled. As a result, the dynamical behaviors of the average displacement, photons, and phonons are radically changed in different regimes. Our study shows that $mathcal{PT}$-symmetric optomechanical devices can serve as a powerful tool for the manipulation of mechanical motion, photons, and phonons.
In the last few years, the great utility of PT-symmetric systems in sensing small perturbations has been recognized. Here, we propose an alternate method relevant to dissipative systems, especially those coupled to the vacuum of the electromagnetic f ields. In such systems, which typically show anti-PT symmetry and do not require the incorporation of gain, vacuum induces coherence between two modes. Owing to this coherence, the linear response acquires a pole on the real axis. We demonstrate how this coherence can be exploited for the enhanced sensing of very weak anhamonicities at low pumping rates. Higher drive powers ($sim 0.1$ W), on the other hand, generate new domains of coherences. Our results are applicable to a wide class of systems, and we specifically illustrate the remarkable sensing capabilities in the context of a weakly anharmonic Yttrium Iron Garnet (YIG) sphere interacting with a cavity via a tapered fiber waveguide. A small change in the anharmonicity leads to a substantial change in the induced spin current.
In this paper, we consider a typical continuous two dimensional $cal PT$-symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the $eta$-inner products. Despite the continuity of Hamiltonian, the $et a$-inner product is not continuous in some sense. It is shown that the difference between the $eta$-inner products of broken and unbroken $cal PT$-symmetry is lower bounded. Moreover, such a property can lead to an uncertainty relation.
We introduce the notion of a ${cal PT}$-symmetric dimer with a $chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.
The dilation method is an important and useful way in experimentally simulating non-Hermitian, especially $cal PT$-symmetric systems. However, the time dependent dilation problem cannot be explicitly solved in general. In this paper, we consider a sp ecial two dimensional time dependent $cal PT$-symmetric system, which is initially set in the unbroken $cal PT$-symmetric phase and later goes across the exceptional point and enters the broken $cal PT$-symmetric phase. For this system, the dilation Hamiltonian and the evolution of $cal PT$-symmetric system are analytically worked out.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا