Engineering geometric phase in semiconductor microcavities S. Abdel-Khalek a,b , K. Berrada c,d,n , H. Eleuch e , M. Abdel-Aty a,f a Mathematics Department, Faculty of Science, Sohag University, Egypt b Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia c Al Imam Mohammad Ibn Saud Islamic University (IMSIU), College of Science, Department of Physics, Riyadh, Saudi Arabia d The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste, Italy e Department of Physics, McGill University, Montreal, Canada H3A 2T8 f University of Science and Technology at Zewail City, Sheikh Zayed District,12588, 6th of October, Egypt HIGHLIGHTS  Geometric phase in semiconductor microcavities.  Dynamics of geometric phase in cavity dissipation.  Solution of master equation of the system under certain conditions.  Effect of excitonic spontaneous emission.  Control of the geometric phase evolution and system dynamics. article info Article history: Received 16 February 2013 Received in revised form 22 February 2014 Accepted 9 July 2014 Available online 17 July 2014 Keywords: Geometric phase Semiconductor microcavity Excitonic spontaneous emission Phase shift Dissipation abstract We present rigorous investigations of the geometric phase in semiconductor microcavities. The effects of excitonic spontaneous emission, initial state setting and cavity dissipation have been discussed. It is shown that the geometric phase decays exponentially due to the presence of excitonic spontaneous emission. More importantly, the inclusion of the phase shift leads to an enhanced sensitivity for the control of the geometric phase evolution and system dynamics. & 2014 Elsevier B.V. All rights reserved. 1. Introduction In recent years much attention has been paid to the quantum phases such as the Pancharatnam phase which was introduced in 1956 by Pancharatnam [1] in his studies of interference effects of polarized light waves. The geometric phase (Berry phase) which was realized in 1984 by Berry [2] is a generic feature of quantum mechanics, and it depends on the chosen path in the space spanned by all the likely quantum states for the system. The definition of phase change for partial cycles was obtained by Jordan [3]. The ideas of Pancharatnam were also used by Samuel and Bhandari [4,5] to show that for the appearance of Panchar- atnam's phase the system needs to be neither unitary nor cyclic [6,7], and may be interpreted by quantum measurements. Presently the models of quantum computation in which a state is an operator of density matrix are developed [8]. It is shown [9] that the geometric phase shift can be used for generating fault- tolerance phase shift gates in quantum computation. Many gen- eralizations have been proposed to the original definition [10–13]. The quantum phase, including the total phase as well as its dynamical and geometric parts, of Pancharatnam type is derived for a general spin system in a time-dependent magnetic field based on the quantum invariant theory [14]. Another approach that provides a unified way to discuss geometric phases in both photon (massless) and other massive particle systems was devel- oped by Lu [15]. Also, an expression for the Pancharatnam phase for the entangled state of a two-level atom interacting with a single mode in an ideal cavity with the atom undergoing a two- photon transition was studied [13]. To bring the two-photon processes closer to the experimental realization, the effect of the dynamic Stark shift in the evolution of the Pancharatnam phase Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/physe Physica E http://dx.doi.org/10.1016/j.physe.2014.07.009 1386-9477/& 2014 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: kberrada@ictp.it (K. Berrada). Physica E 64 (2014) 112–116