Coherent Control of Quantum Dots
This project aims to develop techniques for the preparation, manipulation and measurement of quantum states of semiconductor quantum dots. We aim to realise quantum mechanical concepts in the solid-state. The motivation for this work is both to study the underlying physics, and to implement processes required for quantum information processing and quantum computing.
|Academic Staff:||Mark Fox
|PhD Students:||Tim Godden
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This project is part of the Quantum Information Processing Interdisciplinary Research Collaboration.
The concept of quantum computation is to encode information in an array of two-level quantum mechanical systems known as qubits. A sequence of logic gate operations is performed on the qubits, much like in a classical computer. However, quantum mechanical effects such as entanglement and superposition may be exploited in a quantum computer to provide a massive increase in processing power.
In our well-equipped, modern laboratory, we perform coherent control experiments on single InGaAs/GaAs quantum dots at low temperature, using a photocurrent detection method. Optical control is achieved using pulses from an ultrafast pulsed titanium:sapphire laser, and pulse-shaping techniques. For sample growth and processing, we have access to the cutting edge cleanroom facilities at the EPSRC National Centre for III-V Technologies in Sheffield.
We have recently published work on spin-based and exciton-based qubits, including the observation of interference and the demonstration of a two-qubit quantum logic gate.
The ground-state neutral exciton transition of a single InGaAs quantum dot forms an artificial two-level atom, which may be used to represent a qubit, with the crystal ground state and the single electron-hole pair (exciton) state corresponding to the logical 'zero' and 'one' states respectively. In general the quantum dot state is described by a quantum mechanical superposition. The superposition state can be controlled using a tailored optical field, via the electric-dipole interaction which mixes the exciton state and crystal ground state.
The sample consists of a low density layer of self-assembled InGaAs/GaAs quantum dots embedded in a photodiode structure, grown by molecular beam epitaxy. Under an applied electric field the electron-hole pair tunnel from the dot and are detected as a photocurrent, which is proportional to the final exciton population (see figure 3.) The device is held at low temperature in a helium-flow cryostat, and a sequence of picosecond laser pulses is used to control the dot state. The pulses are focussed onto sub-micron apertures in a shadow mask to spatially isolate single dots.
Resonant excitation with high intensity laser pulses drives Rabi rotations between states, due to the competition between absorption and stimulated emission. Figure 4 shows photocurrent measured as a function of the pulse area of a pulse resonant with the ground to exciton state transition. The pulse area is a quantity proportional to the square root of the power, scaled so that the first maximum occurs at a pulse area of 1 pi (known as a pi-pulse.) A damped oscillation between the two states is observed up to 8 pi. The laser pulse may be used to create an arbitrary superposition state.
- Fast Optical Preparation, Control, and Readout of a Single Quantum Dot Spin
A. J. Ramsay, S. J. Boyle, R. S. Kolodka, J. B. B. Oliviera, J. Skiba-Szymanska, H. Y. Liu, M. Hopkinson, A. M. Fox, and M. Skolnick
Physical Review Letters 100 197401 (2008) http://link.aps.org/abstract/PRL/v100/e197401
We implement a scheme for the preparation, manipulation, and measurement of a single hole spin in a quantum dot, using pulsed optical excitation. This approach combines fast optical control with the long coherence times available with spin-based qubits.
First, a preparation pulse (a pi-pulse resonant with the ground to exciton state transition,) creates a neutral exciton. Under an applied electrical field, the electron quickly tunnels out of the dot, leaving the longer-lived hole in the dot. By exciting with circularly polarized light, a spin up or down exciton (and therefore hole) can be prepared. This spin-polarized hole state can then be probed by a second 'control' laser pulse, resonant with the hole to positively-charged trion (an electron coupled to two holes) transition.
Figure 5 shows the change in photocurrent as a function of the pulse area of the control pulse. The result is dependent on the orientation of the hole spin and the control pulse polarization: A Rabi rotation between the hole and trion states is observed, but only if the control pulse has the opposite circular polarization to the preparation pulse. Pauli blocking suppresses the transition for co-circularly polarized pulses. A control pulse with a pulse area of pi therefore provides a photocurrent read-out of the hole spin state. A 2pi-pulse returns the dot to the single hole state, but also applies a relative phase shift of pi to the targeted spin state, implementing a sigma-z gate.
- Inversion recovery of single quantum-dot exciton based qubit
R. S. Kolodka, A. J. Ramsay, J. Skiba-Szymanska, P. W. Fry, H. Y. Liu, A. M. Fox and M. S. Skolnick
Physical Review B 75 193306 (2007) http://link.aps.org/abstract/PRB/v75/e193306
Here, the coherence decay of a single exciton-qubit is studied. In figure 6, photocurrent is measured as a function of the interferometrically precise time-delay between two resonant time-separated pulses, with a pulse-area of pi/2. The first pulse creates an equal superposition of exciton and crystal ground-states. The second pulse will create a similar superposition, but with a relative phase defined by the time-delay. The excitonic polarisations created by the two pulses interfere resulting in an oscillation in the photocurrent at a frequency equal to the exciton transition. The envelope indicates the loss of coherence of the exciton state, due mostly to electron tunnelling.
Here you may view Roman Kolodka's conference presentation on the Coherent dynamics of a single quantum dot exciton embedded in a photodiode.
- Two-qubit conditional quantum-logic operation in a single self-assembled quantum dot
S. J. Boyle, A. J. Ramsay, F. Bello, H. Y. Liu, M. Hopkinson, A. M. Fox, and M. S. Skolnick
Physical Review B 78 075301 (2008) http://link.aps.org/abstract/PRB/v78/e075301
We implement an optically-gated two-qubit conditional logic operation, the controlled rotation (CROT) gate, in the exciton-biexciton system of a single self-assembled quantum dot. Conditional logic gates such as this are an essential component of any quantum computing scheme. The CROT gate acts on a register of two qubits, labelled control and target, rotating the state of the target qubit through an angle of pi if the control qubit is in the 'one' state.
The two excitons in the exciton-biexciton system, which are distinguishable by their polarization, provide such a two-qubit register. A polarized pi-pulse, resonant with the exciton-biexciton transition, executes the CROT logic, rotating the target exciton state if the control exciton is already present.
This is shown in figure 7, where the change in photocurrent is given as a function of the pulse area of a polarized pulse, resonant with the exciton-biexciton transition. In case (a), a preparation pulse creates the control exciton, before the measurement pulse drives a Rabi rotation between the control exciton and biexciton states. In case (b), the target exciton is prepared, and polarization selection rules prevent creation of the biexciton; a flat signal is therefore measured. Finally, in case (c) no exciton is prepared, and no response is detected as the measurement pulse is off-resonance with any available transition.
Click the following links to see Stephen Boyle's conference talk and poster on the CROT gate, presented at the 29th International Conference on the Physics of Semiconductors, Rio de Janeiro, Brazil (2008), and the One Day Quantum Dot Meeting, Imperial College London, 11 January (2008), respectively.
- Beating of Exciton-Dressed States in a Single Semiconductor InGaAs/GaAs Quantum Dot
S. J. Boyle, A. J. Ramsay, A. M. Fox, M. S. Skolnick, A. P. Heberle, and M. Hopkinson
Physical Review Letters 102 207401 (2009) http://link.aps.org/abstract/PRL/v102/e207401
Coherent light-matter interactions are often understood in terms of dressed states: states that are a composite of light and matter. Recently, we have made a number of experiments to time-resolve the excitonic dressed states of a single self-assembled InAs quantum dot. We demonstrate the possibility of controlling the composition, and energies of the excitonic dressed states on a picosecond timescale. Furthermore, an experiment illustrating that a Rabi oscillation may be interpreted as a beat between two dressed states was performed.