Subramanian Krishnamurthy

Ultra-low power, Zeno effect based optical modulation in a degenerate V-system with a tapered nano fiber in atomic vapor

We demonstrate an ultra-low light level optical modulator using a tapered nano fiber embedded in a hot rubidium vapor. The control and signal beams are co-propagating but orthogonally polarized, leading to a degenerate V-system involving coherent superpositions of Zeeman sublevels. The modulation is due primarily to the quantum Zeno effect for the signal beam induced by the control beam. For a control power of 40 nW and a signal power of 100 pW, we observe near 100% modulation. The ultra-low power level needed for the modulation is due to a combination of the Zeno effect and the extreme field localization in the evanescent field around the taper.

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. To find solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2 × N2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a 15-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.

High efficiency optical modulation at a telecom wavelength using the quantum Zeno effect in a ladder transition in Rb atoms.

We demonstrate a high-efficiency optical modulator at ~1323 nm using the quantum Zeno effect in a ladder transition in a Rb vapor cell. The lower leg of the transitions represents the control beam while the upper leg of the transitions represents the signal beam. The cross-modulation of the signal beam transmission is observed as the control beam is intensity modulated, and is explained in terms of the quantum Zeno effect. We observe a modulation depth of near 100% at frequencies up to 1 MHz and demonstrate modulation at speeds up to 75 MHz, with a 3 dB bandwidth of about 5 MHz, limited by the homogeneous linewidth of the intermediate state. We also describe how much higher modulation speeds could be realized by using a buffer gas to broaden the transitions. We identify and explain the special conditions needed for optimizing the modulation efficiency. Numerical simulations of modulation at ~1 GHz are presented. The maximum modulation speed is found to scale with the pressure-broadened linewidth of the intermediate state, so that much higher speeds should be attainable.

Optically controlled polarizer using a ladder transition for high speed Stokesmetric Imaging and Quantum Zeno Effect based optical logic.

We demonstrate an optically controlled polarizer at ~1323 nm using a ladder transition in a Rb vapor cell. The lower leg of the 5S(1/2),F = 1->5P(1/2),F = 1,2->6S(1/2),F = 1,2 transitions is excited by a Ti:Sapphire laser locked to a saturated absorption signal, representing the control beam. A tunable fiber laser at ~1323 nm is used to excite the upper leg of the transitions, representing the signal beam. When the control beam is linearly polarized, it produces an excitation of the intermediate level with a particular orientation of the angular momentum. Under ideal conditions, this orientation is transparent to the signal beam if it has the same polarization as the control beam and is absorbed when it is polarized orthogonally. We also present numerical simulations of the system using a comprehensive model which incorporates all the relevant Zeeman sub-levels in the system, and identify means to improve the performance of the polarizer. A novel algorithm to compute the evolution of large scale quantum system enabled us to perform this computation, which may have been considered too cumbersome to carry out previously. We describe how such a polarizer may serve as a key component for high-speed Stokesmetric imaging. We also show how such a polarizer, combined with an optically controlled waveplate, recently demonstrated by us, can be used to realize a high speed optical logic gate by making use of the Quantum Zeno Effect. Finally, we describe how such a logic gate can be realized at an ultra-low power level using a tapered nanofiber embedded in a vapor cell.

High-speed modulation in ladder transitions in Rb atoms using high-pressure buffer gas.

Modulators using atomic systems are often limited in speed by the rate of spontaneous emission. One approach for overcoming this limit is to make use of a buffer gas such as Ethane, which causes rapid fine structure mixing of the P(1/2) and P(3/2) states, and broadens the absorption spectra of the D1 and D2 lines in alkali atoms. Employing this effect, we show that one can achieve high speed modulation using ladder transitions in Rubidium. We demonstrate a 100-fold increase, due to the addition of the buffer gas, in the modulation bandwidth using the 5S-5P-5D cascade system. The observed bandwidth of ~200 MHz is within a factor of 2.5 of the upper bound of ~0.51 GHz for the system used, and is limited by various practical constraints in our experiment. We also present numerical simulations for the system and predict that a much higher modulation speed should be achievable under suitable conditions. In combination with a tapered nano fiber or a SiN waveguide, it has the potential to be used for high-speed, low-power all-optical modulation.

Optically controlled waveplate at a telecom wavelength using a ladder transition in Rb atoms for all-optical switching and high speed Stokesmetric imaging

We demonstrate an optically controlled waveplate at ~1323 nm using the 5S(1/2)-5P(1/2)-6S(1/2) ladder transition in a Rb vapor cell. The lower leg of the transitions represents the control beam, while the upper leg represents the signal beam. We show that we can place the signal beam in any arbitrary polarization state with a suitable choice of polarization of the control beam. Specifically, we demonstrate a differential phase retardance of ~180 degrees between the two circularly polarized components of a linearly polarized signal beam. We also demonstrate that the system can act as a Quarter Wave plate. The optical activity responsible for the phase retardation process is explained in terms of selection rules involving the Zeeman sublevels. As such, the system can be used to realize a fast Stokesmetric imaging system with a speed of ~3 MHz. When implemented using a tapered nano fiber embedded in a vapor cell, this system can be used to realize an ultra-low power all-optical switch as well as a Quantum Zeno Effect based all-optical logic gate by combining it with an optically controlled polarizer, previously demonstrated by us. We present numerical simulations of the system using a comprehensive model which incorporates all the relevant Zeeman sub-levels in the system, using a novel algorithm recently developed by us for efficient computation of the evolution of an arbitrary large scale quantum system.

All-optical switch at telecom wavelength based on the quantum zeno effect (QZE)

We present experimental realizations and numerical simulations of an optically controlled Polarizer and Waveplate at telecom wavelength using ladder transitions in 87Rb. When combined, it can be used to realize a QZE based all-optical switch.

Ultra-low Power, Buffer Gas assisted High Speed Optical Modulator in Rb using Tapered Nano Fiber

We report on the experimental progress of an ultra-low power, high speed optical modulator in a tapered nano fiber system using buffer gas induced line broadening of ladder transitions in Rb atoms.

Ultra-low Power Optical Modulation within Tapered Nano-fiber using 5S-5P-5D Ladder Transition of Rb Atoms

We show, theoretically and experimentally, how an optical modulator can be realized within 5S-5P-5D ladder transition of Rb atoms inside a tapered nano-fiber.

Atto-Joules, High Bandwidth All Optical Modulation with a Nano-Fiber Embedded in Alkali Vapor

We report an all-optical modulator with 75 photons at 2 GHz, using a tapered nanofiber embedded in an alkali vapor. The switching energy is 19 atto-Joules, a record low value for modulation at this speed.