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Conference on Lasers and Electro-Optics

Ultra-Fast Quantum Dot Inversion and Switching in a Structured Electromagnetic Vacuum

Xun Ma, Sajeev John

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We demonstrate a novel ultra-fast high-contrast switching mechanism of two-level atoms driven by milliwatt picosecond pulse trains in PBG circuits with step-shaped density of states profiles. Possible application as low-threshold, multi-wavelength-channel all-optical transistors is discussed.
DOI
10.1364/iqec.2009.ithe2

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We demonstrate dynamical near-complete inversion switching of a two-level quantum dot driven by picosecond optical pulses in a bimodal photonic band gap (PBG) waveguide at microwatt power levels. This is enabled by a sharp steplike discontinuity in the local (electromagnetic) density of states (LDOS) provided by a cutoff in one of the two waveguide modes. The atomic Bloch vector equations in this colored vacuum are derived using dressed state description of the atomic density operator in the presence of phonon-mediated dephasing. Instead of assuming phenomenological decay rates, we derive explicit expressions for decay terms of bare state atomic dipole moments and population in the Born-Markov approximation from a master equation approach. Giant Mollow splitting of the atom level due to subwavelength light localization of strong driving pulse causes the time-dependent Mollow bands to straddle the LDOS jump, leading to different radiative decay rates in the upper and lower Mollow sidebands. This results in remarkable field-dependent spontaneous emission and dipolar dephasing rates, combined with a novel ``vacuum structure'' term in the Bloch equations. Our Bloch equations predict ultrafast high-contrast inversion switching that is activated and deactivated by picosecond pulse trains detuned below and above the atomic resonance, respectively. This dynamic inversion is due to the rapid rise in relaxation rates as the pulse amplitude rises, causing the Bloch vector to switch from antiparallel to parallel alignment with the pulse ``torque vector.'' Subsequent near-complete inversion occurs through an adiabatic following process retained long after the pulse amplitude subsides and the system reverts to slow relaxation. For a 1% inhomogeneously broadened distribution of quantum dot with average of 100 D dipole moment, driven by $1.5\text{ }\ensuremath{\mu}\text{m}$ picosecond pulses and coupled to a cutoff mode LDOS jump with radiative emission rates of ${\ensuremath{\gamma}}_{high}=2.5\text{ }\text{THz}$ and ${\ensuremath{\gamma}}_{low}=5\text{ }\text{GHz}$, a large average population switching contrast of 0.5 is demonstrated with a phonon dephasing rate ${\ensuremath{\gamma}}_{p}=0.5\text{ }\text{THz}$. A 1.6 fJ control pulse is required per switching operation and a $30\text{ }\ensuremath{\mu}\text{W}$ pulse train is sufficient to maintain the inversion. This switchable gain (loss) segment of the PBG waveguide can be used to controllably amplify (absorb) signal pulses conveying optical information. This provides a robust mechanism for ultrafast multiwavelength channel all-optical logic in PBG microchips.
We demonstrate picosecond, high-contrast population flipping of two-level atoms interacting with femtojoule optical pulses in a 3D photonic band gap waveguide. This is the result of giant Mollow splitting caused by strong light localization and a remarkable field-dependent relaxation of the atomic Bloch vector as it evolves near an abrupt jump in the electromagnetic density of states. Unlike steady-state switching, population inversion can remain nearly complete after the pulse subsides. This may be used for multiwavelength channel, all-optical, on-chip information processing.
In this thesis, we demonstrate a new type of resonant, nonlinear, light-matter interaction facilitated by the unique electromagnetic vacuum density-of-state (DOS) structure of Photonic Band Gap (PBG) materials. Strong light localization inside PBG waveguides allows extremely strong coupling between laser fields and embedded two-level quantum dots (QD). The resulting Mollow splitting is large enough to traverse the precipitous DOS jump created by a waveguide mode cutoff. This allows the QD Bloch vector to sense the non-smoothness of the vacuum structure and evolve in novel ways that are forbidden in free space. These unusual strong-coupling effects are described using a "vacuum structure term" of the Bloch equation, combined with field-dependent relaxation rates experienced by the QD Bloch vector. This leads to alternation between coherent evolution and enhanced relaxation. As a result, dynamic high-contrast switching of QD populations can be realized with a single beam of picosecond pulses. During enhanced relaxation to a slightly inverted steady state at the pulse peak, the Bloch vector rapidly switches from anti-parallel to parallel alignment with the pulse torque vector. This then leads to a highly inverted state through subsequent coherent "adiabatic following" near the pulse tail, providing a robust mechanism for picosecond, femto-Joule all-optical switching. The simultaneous input of a second, weaker (signal) driving beam at a different frequency on top of the stronger (holding) beam enables rich modulation effects and unprecedented coherent control over the QD population. This occurs through resonant coupling of the signal pulse with the Mollow sideband transitions created by the holding pulse, leading to either augmentation or negation of the final QD population achieved by the holding pulse alone. This effect is applied to ultrafast all-optical logic AND, OR and NOT gates in the presence of significant (0.1 THz) nonradiative dephasing and (about 1%) inhomogeneous broadening. Further numerical studies of pulse evolutions inside the proposed devices demonstrate satisfactory population contrast within a PBG waveguide length of about 10 micro meter. These results provide the building blocks for low-power, ultrafast, multi-wavelength channel, on-chip, all-optical computing.
We study the detailed propagative characteristics of optical pulses in photonic band-gap (PBG) waveguides, coupled near resonantly to inhomogeneously broadened distributions of quantum dots. The line centers of the quantum-dot (QD) distributions are placed near a sharp discontinuity in the local electromagnetic density of states. Using finite-difference time-domain (FDTD) simulations of optical pulse dynamics and independent QD susceptibilities associated with resonance fluorescence, we demonstrate subpicosecond switching from pulse absorption to pulse amplification using steady-state optical holding and gate fields with power levels on the order of 1 milliwatt. In the case of collective response of QDs within the periodic dielectric microstructure, the gate power level is reduced to 200 microwatt for room temperature operation. In principle, this enables 200 Gbits per second optical information processing at wavelengths near 1.5 microns in various wavelength channels. The allowed pulse bandwidth in a given waveguide channel exceeds 0.5 THz allowing switching of subpicosecond laser pulses without pulse distortion. The switching contrast from absorption to gain is governed by the QD oscillator strength and dipole dephasing time scale. We consider dephasing time scales ranging from nanoseconds (low-temperature operation) to one picosecond (room-temperature operation). This all-optical transistor action is based on simple Markovian models of single-dot and collective-dot inversion and switching by coherent resonant pumping near the photon density of states discontinuity. The structured electromagnetic vacuum is provided by two-mode waveguide architectures in which one waveguide mode has a cutoff that occurs, with very large Purcell factor, near the QDs resonance, while the other waveguide mode exhibits nearly linear dispersion for fast optical propagation and modulation. Unlike optical switching based on Kerr nonlinearities in an optical cavity resonator, switching power levels and switching speeds for our QD device are not inversely proportional to cavity quality factors.
We describe all-optical transistor action in photonic band gap materials doped with active atoms. In the presence of a photonic band gap (PBG) material, a coherent laser beam with the frequency slightly detuned from the resonant atomic transition frequency can drive a collection of two-level atoms to an almost totally inverted state, a phenomenon strictly forbidden in ordinary vacuum. By changing the laser field intensity in the neighborhood of a threshold value, it is possible to drive the atomic system through a transition from states in which the atoms populate preferentially the ground level to almost totally inverted states. In this process, the atomic system switches from a passive medium (highly absorptive) to a active medium (highly amplifying). The switching action in a PBG material is not associated with operating near a narrow cavity resonance with conventional trade-off between switching time and switching threshold intensity. Rather it is associated with an abrupt discontinuity in the engineered broad band electromagnetic density of states of the PBG material. We demonstrate all-optical transistor action in PBG materials by analyzing the absorption spectrum of a second probe laser beam and we show that the probe beam experience a substantial differential gain by slight intensity modulations in the control laser field.