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Physical Review Letters

Ultrafast Population Switching of Quantum Dots in a Structured Vacuum

Xun Ma, Sajeev John

Published Dec 3, 2009• 9 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.103.233601

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Switching dynamics and ultrafast inversion control of quantum dots for on-chip optical information processing

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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.

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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.

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We demonstrate a trimodal waveguide architecture in a three-dimensional (3D) photonic-band-gap (PBG) material, in which the local electromagnetic density of states (LDOS) within and adjacent to the waveguide exhibits a forklike wavelength filter characteristic. This facilitates the control and switching of one laser beam with other laser beams ( $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{W}$ steady-state holding power and $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{nW}$ switching power) through mutual coherent resonant interaction with quantum dots. Two waveguide modes provide narrow spectral windows where the electromagnetic LDOS is enhanced by a factor of 100 or more relative to the background LDOS of a third air-waveguide mode with nearly linear dispersion. This ``engineered vacuum'' can be used for frequency-selective, atomic population inversion and switching (by coherent resonant optical pumping) of an inhomogeneously broadened collection of ``atoms'' situated adjacent to the waveguide channel. The ``inverted'' atomic system can then be used to coherently amplify fast optical pulses propagating through the third waveguide mode. This coherent ``control of light with light'' occurs without recourse to microcavity resonances (involving long cavity buildup and decay times for the optical field). Our architecture facilitates steady-state coherent pumping of the atomic system (on the lower-frequency LDOS peak) to just below the gain threshold. The higher-frequency LDOS peak is chosen to coincide with the upper Mollow sideband of the same atomic resonance fluorescence spectrum. The probing laser is adjusted to the lower Mollow sideband, which couples to the linear dispersion (high group velocity part) of the third waveguide mode. This architecture enables rapid modulation (switching) of light at the lower Mollow sideband frequency through light pulses conveyed by the linear dispersion mode at frequencies corresponding to the central Mollow component (lower LDOS peak). We demonstrate that LDOS jumps of order 100 can occur on frequency scales of $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\approx}{10}^{\ensuremath{-}4}{\ensuremath{\omega}}_{c}$ (where ${\ensuremath{\omega}}_{c}$ is the frequency of the jump) in a finite-size 3D photonic crystal (PC) consisting of only $10\ifmmode\times\else\texttimes\fi{}10\ifmmode\times\else\texttimes\fi{}20$ unit cells. When the semiconductor backbone of the PC has a refractive index of 3.5 and ${\ensuremath{\omega}}_{c}$ corresponds to a wavelength of $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, this vacuum engineering may be achieved in a sample whose largest dimension is about $12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$.

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Physical Review A•Dec 17, 2007•28 citations
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.
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.
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 theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.
We demonstrate multiwavelength channel optical logic operations on the Bloch vector of a quantum two-level system in the structured electromagnetic vacuum of a bimodal photonic crystal waveguide. This arises through a bichromatic strong-coupling effect that enables unprecedented control over single quantum-dot (QD) excitation through two beams of ultrashort femtojoule pulses. The second driving pulse (signal) with slightly different frequency and weaker strength than the first (holding) pulse leads to controllable strong modulation of the QD Bloch vector evolution path. This occurs through resonant coupling of the signal pulse with the Mollow sideband transitions created by the holding pulse. The movement of the Mollow sidebands during the passage of the holding pulse leads to an effective chirping in transition frequency seen by the signal. Bloch vector dynamics in the rotating frame of the signal pulse and within the dressed-state basis created by the holding pulse reveals that this chirped coupling between the signal pulse and the Mollow sidebands leads to either augmentation or negation of the final quantum-dot population (after pulse passage) compared to the outcome of the holding pulse alone and depending on the relative frequencies of the pulses. By making use of this extra degree of freedom for ultrafast control of QD excitations, applications in ultrafast all-optical logic and, or, and not gates are proposed in the presence of significant (0.10.10.1) THz nonradiative dephasing and (about 1%) inhomogeneous broadening.
We demonstrate a trimodal waveguide architecture in a three-dimensional (3D) photonic-band-gap (PBG) material, in which the local electromagnetic density of states (LDOS) within and adjacent to the waveguide exhibits a forklike wavelength filter characteristic. This facilitates the control and switching of one laser beam with other laser beams ( $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{W}$ steady-state holding power and $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\mathrm{nW}$ switching power) through mutual coherent resonant interaction with quantum dots. Two waveguide modes provide narrow spectral windows where the electromagnetic LDOS is enhanced by a factor of 100 or more relative to the background LDOS of a third air-waveguide mode with nearly linear dispersion. This ``engineered vacuum'' can be used for frequency-selective, atomic population inversion and switching (by coherent resonant optical pumping) of an inhomogeneously broadened collection of ``atoms'' situated adjacent to the waveguide channel. The ``inverted'' atomic system can then be used to coherently amplify fast optical pulses propagating through the third waveguide mode. This coherent ``control of light with light'' occurs without recourse to microcavity resonances (involving long cavity buildup and decay times for the optical field). Our architecture facilitates steady-state coherent pumping of the atomic system (on the lower-frequency LDOS peak) to just below the gain threshold. The higher-frequency LDOS peak is chosen to coincide with the upper Mollow sideband of the same atomic resonance fluorescence spectrum. The probing laser is adjusted to the lower Mollow sideband, which couples to the linear dispersion (high group velocity part) of the third waveguide mode. This architecture enables rapid modulation (switching) of light at the lower Mollow sideband frequency through light pulses conveyed by the linear dispersion mode at frequencies corresponding to the central Mollow component (lower LDOS peak). We demonstrate that LDOS jumps of order 100 can occur on frequency scales of $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\approx}{10}^{\ensuremath{-}4}{\ensuremath{\omega}}_{c}$ (where ${\ensuremath{\omega}}_{c}$ is the frequency of the jump) in a finite-size 3D photonic crystal (PC) consisting of only $10\ifmmode\times\else\texttimes\fi{}10\ifmmode\times\else\texttimes\fi{}20$ unit cells. When the semiconductor backbone of the PC has a refractive index of 3.5 and ${\ensuremath{\omega}}_{c}$ corresponds to a wavelength of $1.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, this vacuum engineering may be achieved in a sample whose largest dimension is about $12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$.
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.