Nonclassical properties of coherent light in a pair of coupled anharmonic oscillators Nasir Alam, Swapan Mandal n Department of Physics, Visva-Bharati, Santiniketan 731235, India article info Article history: Received 10 July 2015 Received in revised form 3 September 2015 Accepted 10 September 2015 Keywords: Squeezing antibunching vacuum field quantum state transfer coupled anharmonic oscillators abstract The Hamiltonian and hence the equations of motion involving the field operators of two anharmonic oscillators coupled through a linear one is framed. It is found that these equations of motion involving the non-commuting field operators are nonlinear and are coupled to each other and hence pose a great problem for getting the solutions. In order to investigate the dynamics and hence the nonclassical properties of the radiation fields, we obtain approximate analytical solutions of these coupled nonlinear differential equations involving the non-commuting field operators up to the second orders in anhar- monic and coupling constants. These solutions are found useful for investigating the squeezing of pure and mixed modes, amplitude squared squeezing, principal squeezing, and the photon antibunching of the input coherent radiation field. With the suitable choice of the parameters (photon number in various field modes, anharmonic, and coupling constants, etc.), we calculate the second order variances of field quadratures of various modes and hence the squeezing, amplitude squared, and mixed mode squeezing of the input coherent light. In the absence of anharmonicities, it is found that these nonlinear non- classical phenomena (squeezing of pure and mixed modes, amplitude squared squeezing and photon antibunching) are completely absent. The percentage of squeezing, mixed mode squeezing, amplitude squared squeezing increase with the increase of photon number and the dimensionless interaction time. The collapse and revival phenomena in squeezing, mixed mode squeezing and amplitude squared squeezing are exhibited. With the increase of the interaction time, the monotonic increasing nature of the squeezing effects reveal the presence of unwanted secular terms. It is established that the mere coupling of two oscillators through a third one does not produces the squeezing effects of input coherent light. However, the pure nonclassical phenomena of antibunching of photons in vacuum field modes are obtained through the mere coupling and hence the transfers of photons from the remaining coupled mode. & 2015 Elsevier B.V. All rights reserved. 1. Introduction The availability of high power laser sources is found extremely useful in the development of nonlinear optics, laser spectroscopy and quantum optics. In particular, during the last three decades, we find tremendous progresses in the field of quantum optics. These include the generation of squeezed states [1,2] and photon antibunching of the radiation field [3], etc. According to Heisen- berg, there are always some fluctuations involving the measure- ments of canonically conjugate variables and their product obeys the famous uncertainty relation named after him. Barring the ground state of the harmonic oscillator, the uncertainty product of canonically conjugate variables attains the minimum value for coherent state only. It is established that the fluctuation of the dimensionless quadrature components involving the coherent state is equal and is termed as zero point fluctuations [4]. Before the discovery of squeezed states, the ZPF was regarded as the standard quantum limit (SQL). The squeezed state is a quantum state of the radiation field in which one of the quadrature fluc- tuations goes below the ZPF and hence the SQL [5]. Of course, the uncertainty relation due to Heisenberg is to be respected for the squeezed state as well. The abstract idea of squeezed state came into reality through the remarkable experiment in the degenerate four wave mixing of sodium atom [6]. Till now, we find lot of experimental and theoretical developments involving the re- searches in squeezed state [1,2,7–11]. It is because the squeezed state could be used in the detection of gravitational wave and noise free communication [1,2]. It is claimed that the sensitivity of the LIGO (Laser Interferometer Gravitational wave Observatory) detector is increased in an unprecedented way by using the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications http://dx.doi.org/10.1016/j.optcom.2015.09.034 0030-4018/& 2015 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: swapanvb@rediffmail.com (S. Mandal). Optics Communications 359 (2016) 221–233