A method is proposed for the optical rotation of the spin of an electron in a quantum dot using excited trion states to implement operations significantly faster than those of most existing proposals. Key ingredients are the geometric phase induced by 2pi hyperbolic secant pulses, use of coherently trapped states and use of naturally dark states. Our proposal covers a variety of quantum dots by addressing different parameter regimes. Numerical simulations with typical parameters for InAs self-assembled quantum dots, including their dissipative dynamics, give fidelities of the operations in excess of 99%.
We demonstrate optical control of the geometric phase acquired by one of the spin states of an electron confined in a charge-tunable InAs quantum dot via cyclic 2pi excitations of an optical transition in the dot. In the presence of a constant in-plane magnetic field, these optically induced geometric phases result in the effective rotation of the spin about the magnetic field axis and manifest as phase shifts in the spin quantum beat signal generated by two time-delayed circularly polarized optical pulses. The geometric phases generated in this manner more generally perform the role of a spin phase gate, proving potentially useful for quantum information applications.
Recently, Rostovtsev et al (2009 Phys. Rev. A 79 063833) established an analytical treatment of the detuned atom–field interaction without using the rotating-wave approximation (RWA). Using this result, here we study qualitatively the dynamics of geometric phase (GP) and population transfer in a two-level atom interacting with an external off-resonant classical field for arbitrary pulse shape without using RWA. We use this exact method (without RWA) to reexamine the variation of populations and GP and compare the result with the RWA considering two kinds of the external field. We show that it is possible to control the GP dynamics by choosing suitable parameters of the atom–field system. Interestingly, we find that the variation of the populations and GP in the time is unchanged and it differs as we get further from the resonance. Moreover, we show that the Rabi frequency plays a role in reduction or augmentation of the periodic time interval for the GP. The solution is very suitable for atom–field systems, especially when the system is far from the resonance so that the RWA method breaks down.
We investigate geometric-phase control in resonantly driven two-level atoms exposed to near-degenerate dichromatic laser pulses. In contrast to conventional two-color schemes based on widely separated frequencies, the closely spaced frequency components generate a slowly varying beating envelope that repeatedly reverses the pseudo-spin rotation on the Bloch sphere. This enables coherent control of the geometric phase accumulated during Rabi dynamics and strongly modifies the resulting photoelectron spectra. Using an exactly solvable model for flat-top pulse envelopes, we derive the essential-state dynamics analytically and analyze photoionization induced both by an auxiliary field and by the dichromatic driving field itself. We show that the formation of Autler--Townes doublets can be interpreted in terms of destructive interference associated with geometric phases acquired during completed pseudo-spin rotations. Beyond the canonical Autler--Townes regime, beat-induced reversal dynamics lead to qualitatively different spectral structures, including re-emergent central peaks and higher-order sidebands. These effects originate from the nonuniform temporal evolution induced by the beating envelope, which modifies the balance between positive and negative excitation amplitudes. Our results establish beating-field control as a route toward engineering geometric-phase interference in ultrafast light--matter interactions and suggest broader applications in coherent control of atoms, molecules, and x-ray-driven systems.
It has been known since the early days of quantum mechanics that hyperbolic secant pulses possess the unique property that they can perform full-cycle Rabi oscillations on two-level quantum systems independently of the pulse detuning. More recently, it was realized that they induce detuning-controlled phases without changing state populations. Here, we experimentally demonstrate the properties of hyperbolic secant pulses on superconducting transmon qubits and contrast them with the more commonly used Gaussian and square waves. We further show that these properties can be exploited to implement phase gates, nominally without exiting the computational subspace. This enables us to demonstrate a microwave-driven
Z rotation with a single control parameter, the detuning.
Quantum dots are attractive due to their potential technological applications and the opportunity they provide for study of fundamental physics in the mesoscopic scale. This dissertation studies optically controlled spins in quantum dots in connection to quantum information processing. The physical realization of the quantum bit (qubit) consists of the two spin states of an extra electron confined in a quantum dot. Spin rotations are performed optically, by use of an intermediate charged exciton (trion) state. The two spin states and the trion form a
Lambda-type system. The merits of this system for quantum information processing include integrability into a solid-state device, long spin coherence time, and fast and focused optical control. In this dissertation, we study the optical decay mechanisms of the trion state in the quantum dot. Using a master-equation approach, we derive microscopically the optical decay of the three- level system and find a novel term, the so-called spontaneously generated coherence (SGC). The latter, though predicted more than a decade ago for atomic
Lambda-systems satisfying certain conditions, had not been detected yet in any system. We found that in quantum dots, these conditions can be satisfied. We present the experiment which, in collaboration with our theory, constituted the first measurement of SGC. We establish the unification of SGC, polarization entanglement, and two- pathway decay. By keeping track of the spontaneously emitted photon dynamics, we find the conditions on the couplings that determine which effect will take place. We have thus placed SGC in a more quantum informational framework, characterizing it as lack of entanglement between the emitted photon and the three-level system. We develop a theory of ultrafast optical single-qubit rotations by use of 2
pi pulses, which have the two-fold advantage of minimal trion excitation and negligible spin precession. The analytically solvable hyperbolic secant pulses of Rosen and Zener for the two-level system are investigated in the context of the three-level system. Ultrafast rotations about the quantum dot growth direction are designed, the angle of spin rotation is expressed analytically, and the fidelity is studied by simulations. Adaptive feedback loops are employed to correct for unintended dynamics