H. Jing, Z. Geng, S. K. Özdemir, J. Zhang, X.-Y. Lü, B. Peng, L. Yang, F. Nori

Optomechanically-induced transparency (OMIT) and the associated slow-light propagation provide the basis for storing photons in nanofabricated phononic devices. Here we study OMIT in parity-time (PT)-symmetric microresonators with a tunable gain-to-loss ratio. This system features a reversed, non-amplifying transparency: inverted-OMIT. When the gain-to-loss ratio is steered, the system exhibits a transition from the PT-symmetric phase to the broken-PT-symmetric phase. We show that by tuning the pump power at fixed gain-to-loss ratio or the gain-to-loss ratio at fixed pump power, one can switch from slow to fast light and vice versa. Moreover, the presence of PT-phase transition results in the reversal of the pump and gain dependence of transmission rates. These features provide new tools for controlling light propagation using optomechanical devices.

http://arxiv.org/abs/1411.7115

Quantum Physics (quant-ph); Optics (physics.optics)

Baogang Zhu, Rong Lu, Shu Chen

We study the parity- and time-reversal PT symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model with two conjugated imaginary potentials \(\pm i\gamma\) at two end sites. The SSH model is known as one of the simplest two-band topological models which has topologically trivial and nontrivial phases. We find that the non-Hermitian terms can lead to different effects on the properties of the eigenvalues spectrum in topologically trivial and nontrivial phases. In the topologically trivial phase, the system undergos an abrupt transition from unbroken PT-symmetry region to spontaneously broken \(\mathcal{PT}\)-symmetry region at a certain \(\gamma_{c}\), and a second transition occurs at another transition point \(\gamma_{c^{‘}}\) when further increasing the strength of the imaginary potential \(\gamma\). But in the topologically nontrivial phase, the zero-mode edge states become unstable for arbitrary nonzero \(\gamma\) and the \(\mathcal{PT}\)-symmetry of the system is spontaneously broken, which is characterized by the emergence of a pair of conjugated imaginary modes.

http://arxiv.org/abs/1405.5591

Other Condensed Matter (cond-mat.other); Quantum Physics (quant-ph)

H. Jing, Sahin K. Ozdemir, Xin-You Lv, Jing Zhang, F. Nori

The parity-time-symmetric structure was experimentally accessible very recently in coupled optical resonators with which, for normal or non-PT-symmetric cases, a phonon laser device had also been realized. Here we study cavity optomechanics of this system now with tunable gain-loss ratio. We find that nonlinear behaviors emerge for cavity-photon populations around balanced point, resulting giant enhancement of both optical pressure and phonon-lasing action. Potential applications range from enhancing mechanical cooling to designing highly-efficient phonon-laser amplifier.

http://arxiv.org/abs/1403.0657

Quantum Physics (quant-ph); Optics (physics.optics)

Xun-Wei Xu, Yu-xi Liu, Chang-Pu Sun, Yong Li

We propose to observe mechanical PT symmetry in the coupled optomechanical systems. In order to provide gain to one mechanical resonator and equivalent amount of damp to another, we drive the two optical cavities with a blue and a red detuned laser fields respectively. After adiabatically eliminating the freedom of the cavity modes, we develop a formalism for describing mechanical PT-symmetric system. Moreover, we discuss the experimental feasibility of our scheme and show that the observation of mechanical PT-symmetric transition in the coupled optomechanical systems is within the reach of resent experiments.

http://arxiv.org/abs/1402.7222

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Optics (physics.optics)

Yi-Chan Lee, Min-Hsiu Hsieh, Steven T. Flammia, Ray-Kuang Lee

Bender et al. have developed PT-symmetric quantum theory as an extension of quantum theory to non-Hermitian Hamiltonians. We show that when this model has a local PT symmetry acting on composite systems it violates the non-signaling principle of relativity. Since the case of global PT symmetry is known to reduce to standard quantum mechanics, this shows that the PT-symmetric theory is either a trivial extension or likely false as a fundamental theory.

http://arxiv.org/abs/1312.3395

Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)

Bo Peng, Sahin Kaya Ozdemir, Fuchuan Lei, Faraz Monifi, Mariagiovanna Gianfreda, Gui Lu Long, Shanhui Fan, Franco Nori, Carl M. Bender, Lan Yang

Optical systems combining balanced loss and gain profiles provide a unique platform to implement classical analogues of quantum systems described by non-Hermitian parity-time- (PT-) symmetric Hamiltonians and to originate new synthetic materials with novel properties. To date, experimental works on PT-symmetric optical systems have been limited to waveguides in which resonances do not play a role. Here we report the first demonstration of PT-symmetry breaking in optical resonator systems by using two directly coupled on-chip optical whispering-gallery-mode (WGM) microtoroid silica resonators. Gain in one of the resonators is provided by optically pumping Erbium (Er3+) ions embedded in the silica matrix; the other resonator exhibits passive loss. The coupling strength between the resonators is adjusted by using nanopositioning stages to tune their distance. We have observed reciprocal behavior of the PT-symmetric system in the linear regime, as well as a transition to nonreciprocity in the PT symmetry-breaking phase transition due to the significant enhancement of nonlinearity in the broken-symmetry phase. Our results represent a significant advance towards a new generation of synthetic optical systems enabling on-chip manipulation and control of light propagation.

http://arxiv.org/abs/1308.4564

Optics (physics.optics); Materials Science (cond-mat.mtrl-sci); Mathematical Physics (math-ph); Classical Physics (physics.class-ph); Quantum Physics (quant-ph)

Sean Nixon, Yi Zhu, Jianke Yang

Nonlinear dynamics of wave packets in PT-symmetric optical lattices near the phase-transition point are analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of novel phenomena known to exist in this envelope equation are shown to also exist in the full equation including wave blowup, periodic bound states and solitary wave solutions.

http://arxiv.org/abs/1208.5995

Optics (physics.optics); Pattern Formation and Solitons (nlin.PS)

Chao Zheng, Liang Hao, Gui Lu Long

Masillo [1] commented on our manuscript [2] “Observation of a Fast Evolution in a Parity-time-symmetric System”, pointing out a contradiction of our work with Ref.[3]. In this reply, we pointed out there is no disagreement between Masillo’s comment and our work in Ref. [2]. The efficiency cost pointed out in Ref.\cite{masillo} exists, namely to obtain the PT-symmetric hamiltonian evolution, one has to make a measurement on the auxiliary qubit and the auxiliary qubit is at state \(\left|0\right \rangle\) only probabilistically. This is reflected in the amplitude of the spectrum in the NMR quantum simulation. As a result, we made a small modification in a new version of the Ref. [2], and Fig. 2 of Ref.[2] has been replaced by spectra of two different \(\alpha\)’s in order to illustrate this fact.

http://arxiv.org/abs/1106.1848

Quantum Physics (quant-ph)

Chao Zheng, Liang Hao, Gui Lu Long

To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In the parity-time-symmetric(PT-symmetric) Hamiltonian theory, it was predicted that the optimized evolution time can be reduced drastically comparing to the bound in the Hermitian case, and can become even zero. In this Letter, we report the experimental observation of the fast evolution of a PT-symmetric Hamiltonian in an nuclear magnetic resonance (NMR) quantum system. The experimental results demonstrate that the PT-symmetric Hamiltonian can indeed evolve much faster than that in a quantum system, and time it takes can be arbitrary close to zero.

http://arxiv.org/abs/1105.6157

Quantum Physics (quant-ph)