(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Reliable, efficient electrically pumped silicon-based lasers would enable full integration of photonic and electronic circuits, but have previously only been realized by wafer bonding. Here, we demonstrate continuous-wave InAs/GaAs quantum dot lasers directly grown on silicon substrates with a low threshold current density of 62.5 A cm–2, a room-temperature output power exceeding 105 mW and operation up to 120 °C. Over 3,100 h of continuous-wave operating data have been collected, giving an extrapolated mean time to failure of over 100,158 h. The realization of high-performance quantum dot lasers on silicon is due to the achievement of a low density of threading dislocations on the order of 105 cm−2 in the III–V epilayers by combining a nucleation layer and dislocation filter layers with in situ thermal annealing. These results are a major advance towards reliable and cost-effective silicon-based photonic–electronic integration.

/pdf/electrically-pumped-continuous-wave-iii-v-quantum-dot-lasers-rmg1qnqnyt.pdf

Electrically pumped continuous-wave III–V quantum dot lasers on silicon

We present, to the best of our knowledge, the first demonstration of coherent solid-state light detection and ranging (LIDAR) using optical phased arrays in a silicon photonics platform. An integrated transmitting and receiving frequency-modulated continuous-wave circuit was initially developed and tested to confirm on-chip ranging. Simultaneous distance and velocity measurements were performed using triangular frequency modulation. Transmitting and receiving optical phased arrays were added to the system for on-chip beam collimation, and solid-state beam steering and ranging measurements using this system are shown. A cascaded optical phase shifter architecture with multiple groups was used to simplify system control and allow for a compact packaged device. This system was fabricated within a 300 mm wafer CMOS-compatible platform and paves the way for disruptive low-cost and compact LIDAR on-chip technology.

Coherent solid-state LIDAR with silicon photonic optical phased arrays

Hybrid silicon lasers based on bonded III–V layers on silicon are currently the best contenders for on-chip lasers for silicon photonics. On-chip silicon light sources are highly desired for use as electrical-to-optical converters in silicon-based photonics. Zhiping Zhou and Bing Yin of Peking University in China and Jurgen Michel of Massachusetts Institute of Technology assess the three main contenders for such light sources: erbium-based light sources, germanium-on-silicon lasers and III-V-based silicon lasers. They consider operating wavelength, pumping conditions, power consumption, thermal stability and fabrication process. The scientists regard the power efficiencies of electrically pumped erbium-based lasers as being too low and the threshold currents of germanium lasers as being too high. They conclude that III–V quantum dot lasers monolithically grown on silicon show the most promise for realizing on-chip lasers.

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On-chip light sources for silicon photonics

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

https://iopscience.iop.org/article/10.1088/1361-6633/aad5b2/pdf

Photonic quantum information processing: a review

We demonstrate record performance 1.3 μm InAs quantum dot lasers grown on silicon by molecular beam epitaxy. Ridge waveguide lasers fabricated from the as-grown material achieve room temperature continuous wave thresholds as low as 16 mA, output powers exceeding 176 mW, and lasing up to 119 °C. P-modulation doping of the active region improves T0 to the range of 100–200 K while maintaining low thresholds and high output powers. Device yield is presented showing repeatable performance across different dies and wafers.

High performance continuous wave 1.3 μm quantum dot lasers on silicon

Direct epitaxial integration of III-V materials on Si offers substantial manufacturing cost and scalability advantages over heterogeneous integration. The challenge is that epitaxial growth introduces high densities of crystalline defects that limit device performance and lifetime. Quantum dot lasers, amplifiers, modulators, and photodetectors epitaxially grown on Si are showing promise for achieving low-cost, scalable integration with silicon photonics. The unique electrical confinement properties of quantum dots provide reduced sensitivity to the crystalline defects that result from III-V/Si growth, while their unique gain dynamics show promise for improved performance and new functionalities relative to their quantum well counterparts in many devices. Clear advantages for using quantum dot active layers for lasers and amplifiers on and off Si have already been demonstrated, and results for quantum dot based photodetectors and modulators look promising. Laser performance on Si is improving rapidly with ...

Perspective: The future of quantum dot photonic integrated circuits

We observe the unconventional photon blockade effect in quantum dot cavity QED, which, in contrast to the conventional photon blockade, operates in the weak coupling regime. A single quantum dot transition is simultaneously coupled to two orthogonally polarized optical cavity modes, and by careful tuning of the input and output state of polarization, the unconventional photon blockade effect is observed. We find a minimum second-order correlation g^{(2)}(0)≈0.37, which corresponds to g^{(2)}(0)≈0.005 when corrected for detector jitter, and observe the expected polarization dependency and photon bunching and antibunching; close by in parameter space, which indicates the abrupt change from phase to amplitude squeezing.

Observation of the Unconventional Photon Blockade.

We review recent advances in the field of quantum dot lasers on silicon. A summary of device performance, reliability, and comparison with similar quantum well lasers grown on silicon will be presented. We consider the possibility of scalable, low size, weight, and power nanolasers grown on silicon enabled by quantum dot active regions for future short-reach silicon photonics interconnects.

Quantum dot lasers for silicon photonics [Invited]

Laser gain regions using quantum dots have numerous improvements over quantum wells for photonic integration. Their atom-like density of states gives them unique gain properties that can be finely tuned by changing growth conditions. The gain bandwidth can be engineered to be broad or narrow and to emit at a wide range of wavelengths throughout the near infrared. The large energy level separation of the dot states from the surrounding material results in excellent high-temperature performance and gain recovery at sub-picosecond timescales. The fact that the quantum dots are isolated from each other and act independently at inhomogeneously broadened wavelengths results in ultralow linewidth enhancement factors, highly stable broadband mode-locked lasers, single-section mode locking, and the possibility of reduced crosstalk between amplified signals at low signal injection and enhanced four-wave mixing at high signal injection. The high carrier confinement and areal dot density provide reduced sensitivity to crystalline defects allowing for long device lifetimes even when epitaxially grown on silicon at high dislocation densities.

Justin Norman

Papers

High performance continuous wave 1.3 μm quantum dot lasers on silicon

Perspective: The future of quantum dot photonic integrated circuits

Observation of the Unconventional Photon Blockade.

Quantum dot lasers for silicon photonics [Invited]

A Review of High-Performance Quantum Dot Lasers on Silicon