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Enhanced coherent control of spin states in a quantum dot using the AC Stark effect

Josiah Ethan Hsi

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

The coherent control of carrier spin states in semiconductor quantum dots (QDs) is a key requirement for certain quantum information applications, particularly where lightmatter interactions are involved such as in the generation of spin-photon entangled states. A widely used approach for spin control involves Larmor precession in an externally applied magnetic field. Increasing the magnetic field strength enhances the spin precession rate, thus improving the photon generation rate. However, this also introduces Zeeman splitting, which lifts the spin-state degeneracy. As a result frequency distinguishability is introduced, reducing the fidelity of the entangled spinphoton states. This work explores a novel approach to mitigate the Zeeman splitting by employing the AC Stark effect via a red-detuned laser. The Stark shift counteracts the Zeeman energy difference, effectively restoring transition degeneracy within the transition linewidth while allowing for an increased magnetic field strength and consequently a faster precession rate. Theoretical modelling demonstrates that this technique enables an almost doubling of the current spin precession frequency while maintaining nearly degenerate optical transitions. To validate this approach, a high-precision optical system is under development to probe QD emission under simultaneous magnetic and optical fields. Simulations incorporating both effects confirm the feasibility of this method for eliminating frequency distinguishability. These results lay the groundwork for the development of scalable quantum dot-based photonic platforms for quantum communication and information processing.

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Hybrid acousto-optical spin control in quantum dots

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The Coherent Optical Spectroscopy and Control of an Electron Spin in a Self-Assembled Quantum Dot for Quantum Computing.

Erik D. Kim

Self-assembled quantum dots (QDs) containing a single electron are one of the leading candidate systems for the realization of a quantum computer. The spin states of charges confined in these dots have been shown to possess a number of qualities that are attractive for use as the quantum bits (qubits) in quantum computing implementations, particularly their long lifetimes and coherence times. In addition, these spin qubits may be controlled optically, offering the prospect of ultrafast qubit gate operations, a crucial necessity for the execution of quantum algorithms. Due to the weak interaction of self-assembled QDs with light, however, the coherent optical control and read-out of the spin states of charged self-assembled QDs has proven to be a considerable challenge. This thesis presents two sets of experiments demonstrating the coherent optical control and read-out of the quantum states of a self-assembled InAs QD containing a single electron. The first utilizes mode-locked picosecond optical pulses to control the optical transitions in the dot and to detect QD level occupations. These capabilities are used to observe transient phenomena in a singly charged InAs QD such as the generation and decay of excited state population and spin precession. Further, Rabi oscillations between the electron and the lowest-lying excited state are observed, demonstrating the ability to coherently control the optical transitions of the QD, a prerequisite for spin control. These results are built upon in the second set of experiments, in which a combination of optical pulses, an externally applied DC magnetic field and a continuous-wave (CW) optical field are employed to initialize and completely control the states of a QD confined electron spin. Spin control by the use of pulse-driven two-photon Raman processes, spin precession about the external magnetic field and geometric phases generated by CW-driven cyclic evolutions in the dot is demonstrated. A number of spin qubit gate operations are shown for these spin control mechanisms, forming a foundational set of single qubit gates required for the implementation of quantum computing with singly charged self-assembled QDs.

•Jan 1, 2009•1 citation
The coherent control of carrier spin states in semiconductor quantum dots (QDs) is a key requirement for certain quantum information applications, particularly where lightmatter interactions are involved such as in the generation of spin-photon entangled states. A widely used approach for spin control involves Larmor precession in an externally applied magnetic field. Increasing the magnetic field strength enhances the spin precession rate, thus improving the photon generation rate. However, this also introduces Zeeman splitting, which lifts the spin-state degeneracy. As a result frequency distinguishability is introduced, reducing the fidelity of the entangled spinphoton states. This work explores a novel approach to mitigate the Zeeman splitting by employing the AC Stark effect via a red-detuned laser. The Stark shift counteracts the Zeeman energy difference, effectively restoring transition degeneracy within the transition linewidth while allowing for an increased magnetic field strength and consequently a faster precession rate. Theoretical modelling demonstrates that this technique enables an almost doubling of the current spin precession frequency while maintaining nearly degenerate optical transitions. To validate this approach, a high-precision optical system is under development to probe QD emission under simultaneous magnetic and optical fields. Simulations incorporating both effects confirm the feasibility of this method for eliminating frequency distinguishability. These results lay the groundwork for the development of scalable quantum dot-based photonic platforms for quantum communication and information processing.
Abstract AC Stark effect, also known as light shift effect, is a dominating factor limiting the long-term stability of the rubidium optical clock. We propose a method of locking the laser loop which allows the Zeeman shift to act as a counterbalance to the light shift. In pursuit of this goal, we show detailed calculations for the excited state Zeeman splitting in the intermediate magnetic field regime (0~G to 12~G) and demonstrate measurements with quantitative spectroscopic data confirming to within ±\pm± 90~kHz/G the predicted Zeeman shift calculations for the Fe=4,mf=−2F_e = 4, m_f = -2Fe​=4,mf​=−2 transition. In this proof-of-concept setup the method of light shift compensation via Zeeman shift control to within 3.5~kHz is demonstrated. Further improvements in the magnetic field control could enhance the accuracy for controlling the light shift effect to well below 1~kHz, limited by noise in the applied Zeeman shift which is proportional to both the stability of the current in the coil and the Zeeman sensitivity of the chosen transition.
Mechanical degrees of freedom very weakly couple to spins in semiconductors. The inefficient coupling between phonons and single electron spins in semiconductor quantum dots (QDs) hinders their integration into on-chip acoustically coupled quantum hybrid systems. We propose a hybrid acousto-optical spin control method that circumvents this problem and effectively introduces acoustic spin rotation to QDs, complementing their rich couplings with external fields and quantum registers. We show that combining continuous-wave detuned optical coupling to a trion state and acoustic modulation results in spin rotation around an axis defined by the acoustic field. The optical field breaks spin conservation, allowing phonons to drive transitions between disrupted spin states when at resonance with the Zeeman frequency. Our method is compatible with pulse sequences that mitigate quasi-static noise effects, which makes trion recombination the primary limitation to gate fidelity under cooled nuclear-spin conditions. Numerical simulations indicate that spin rotation fidelity can be very high, if the trion lifetime is long and Zeeman splitting is sufficiently large, with a currently feasible 50~ns lifetime and 44~GHz splitting giving 99.9\% fidelity. Applying our advancement could enable acoustic QD spin state transfer to diverse solid-state systems and transduction between acoustic, optical, and microwave domains, all within an on-chip integration-ready setting.
Fast, controlled coherent interactions between spins in separated quantum dots are a key requirement for two-qubit gates and distributed architectures in advancing quantum information in the solid state. We have performed two-color pump-probe experiments in which pulsed lasers emitting at different photon energies manipulate two subsets of electron spins in an inhomogeneous ensemble of InGaAs quantum dots. Measurements of the resulting ellipticity demonstrate the slow, power dependent onset of phase shifts in the Larmor precession in a magnetic field of one subset of oriented spins after optical orientation of the second subset. Model calculations show that these results are consistent with a Heisenberg-like interaction between the pairs of spins with strength ~ micro-eV and that this interaction results in entanglement between the spins.
In typical epitaxial quantum dots (QDs) the ideally degenerate optical excitons are energy split, preventing the formation of two-photon entanglement in a biexciton decay. We use an external field, here a continuous-wave laser tuned to the QD in the ac Stark limit, to cancel the splitting and create two-photon entanglement. Quantum-state tomography is used to construct the two-photon density matrix. When the splitting is removed it satisfies well-known entanglement tests. Our approach shows that polarization-entangled photons can be routinely produced in semiconductor nanostructures.
Photonic graph states are key resource states for measurement based quantum information processing. As semiconductor quantum dots are excellent deterministic photon emitters, several protocols using them for the generation of linear cluster states have been proposed, either based on constant precession of a hole or electron spin in a weak magnetic field, or based on optical spin control, in a stronger magnetic field. We theoretically compare four such schemes, using polarization or time-bin encoding, respectively, for a range of cavity environments and spin coherence times. In particular we study how different error mechanisms affect the different schemes, using a microscopic model of the spin control, the excitation and emission dynamics, and of the phonon bath. We find the spin-precession based schemes to scale well with strong cavity enhancement and to be naturally robust against phonon-induced decoherence, while the schemes using optical spin control can perform well for lower spin coherence times and are strongly dependent on the cooperativity of the cavity induced cycling transition. Our results provide a regime map for choosing between magnetic-field-driven and optically controlled protocols depending on spin coherence time, Purcell enhancement, and suppression of unwanted decay channels.
Self-assembled quantum dots (QDs) containing a single electron are one of the leading candidate systems for the realization of a quantum computer. The spin states of charges confined in these dots have been shown to possess a number of qualities that are attractive for use as the quantum bits (qubits) in quantum computing implementations, particularly their long lifetimes and coherence times. In addition, these spin qubits may be controlled optically, offering the prospect of ultrafast qubit gate operations, a crucial necessity for the execution of quantum algorithms. Due to the weak interaction of self-assembled QDs with light, however, the coherent optical control and read-out of the spin states of charged self-assembled QDs has proven to be a considerable challenge. This thesis presents two sets of experiments demonstrating the coherent optical control and read-out of the quantum states of a self-assembled InAs QD containing a single electron. The first utilizes mode-locked picosecond optical pulses to control the optical transitions in the dot and to detect QD level occupations. These capabilities are used to observe transient phenomena in a singly charged InAs QD such as the generation and decay of excited state population and spin precession. Further, Rabi oscillations between the electron and the lowest-lying excited state are observed, demonstrating the ability to coherently control the optical transitions of the QD, a prerequisite for spin control. These results are built upon in the second set of experiments, in which a combination of optical pulses, an externally applied DC magnetic field and a continuous-wave (CW) optical field are employed to initialize and completely control the states of a QD confined electron spin. Spin control by the use of pulse-driven two-photon Raman processes, spin precession about the external magnetic field and geometric phases generated by CW-driven cyclic evolutions in the dot is demonstrated. A number of spin qubit gate operations are shown for these spin control mechanisms, forming a foundational set of single qubit gates required for the implementation of quantum computing with singly charged self-assembled QDs.