تقرير
Experimentally-realizable $\mathcal{PT}$ phase transitions in reflectionless quantum scattering
| العنوان: | Experimentally-realizable $\mathcal{PT}$ phase transitions in reflectionless quantum scattering |
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| المؤلفون: | Soley, Micheline B., Bender, Carl M., Stone, A. Douglas |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics Physics (Other) Quantum Physics |
| مصطلحات موضوعية: | Quantum Physics, Mathematical Physics, Physics - Atomic Physics |
| الوصف: | A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite having purely real potentials. These potentials are one-dimensional, inverted, and unstable and have the form $V(x) = - \lvert x\rvert^p$ ($p>0$), terminated at a finite length or energy to a constant value as $x\to \pm\infty$. The signature of unbroken $\mathcal{PT}$ symmetry is the existence of reflectionless propagating states at discrete real energies up to arbitrarily high energy. In the $\mathcal{PT}$-broken phase, there are no such solutions. In addition, there exists an intermediate mixed phase, where reflectionless states exist at low energy but disappear at a fixed finite energy, independent of termination length. In the mixed phase exceptional points (EPs) occur at specific $p$ and energy values, with a quartic dip in the reflectivity in contrast to the quadratic behavior away from EPs. $\mathcal{PT}$-symmetry-breaking phenomena have not been previously predicted in a quantum system with a real potential and no reservoir coupling. The effects predicted here are measurable in standard cold-atom experiments with programmable optical traps. The physical origin of the symmetry-breaking transition is elucidated using a WKB force analysis that identifies the spatial location of the above-barrier scattering. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevLett.130.250404 |
| URL الوصول: | http://arxiv.org/abs/2209.05426 |
| رقم الأكسشن: | edsarx.2209.05426 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevLett.130.250404 |
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