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 2π 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.PACS numbers: 78.67. Hc, 71.35.Pq, 42.50.Md, 42.50.Hz A single charge confined in an epitaxially grown quantum dot (QD) shows considerable promise as the basic building block in a quantum computing architecture where the spin of the charge serves as the qubit [1][2][3]. Efforts to demonstrate the feasibility of a quantum computer based on such qubits have resulted in a number of achievements towards satisfying the DiVincenzo criteria [4] for quantum computing. Among these achievements are spin readout [5][6][7], the demonstration of long spin coherence times [8][9][10][11], spin initialization [12][13][14][15][16] and the coherent control of electron spins [17][18][19][20][21].Of fundamental importance in executing quantum algorithms is the ability to perform a universal set of unitary operations including arbitrary single qubit operations, one of the requirements that may be met with sequential qubit rotations about two orthogonal axes [22]. Optical approaches to performing these rotations on QD confined spin qubits are attractive as they offer the prospect of ultrafast gates using readily available laser sources [23][24][25][26] and have already demonstrated fast spin rotations about the optical axis [19][20][21].To obtain fast optically driven rotations about a complementary axis, Economou and Reinecke [26] have proposed the use of geometric phases [27] generated by cyclic 2π excitations of the optical transitions of a QD in the presence of an external DC magnetic field applied normal to the optical axis. For a properly tailored pulse, these optically induced geometric phases serve to variably alter the relative phase between the probability amplitudes of the resident spin states. If the resident spin is initially in a coherent superposition of stationary spin states, this change in the relative phase leads to an effective spin rotation about the spin quantization axis, i.e. the axis of the magnetic field. To date, however, such rotations have not been demonstrated, with recent studies [20,21] instead relying upon combinations of pulse driven rotations about the optical axis and spin precession about the magnetic field to vary the rotation axis.In this Report, we demonstrate the use of a narrowbandwidth continuous-wave (CW) optical field (to simulate a long narrow-band pulse) applied between a pair of time-delayed picosecond optical pulses to ...

We study the coupling between a photonic crystal cavity and an off-resonant quantum dot under resonant excitation of the cavity or the quantum dot. Linewidths of the quantum dot and the cavity as a function of the excitation laser power are measured. We show that the linewidth of the quantum dot, measured by observing the cavity emission, is significantly broadened compared to the theoretical estimate. This indicates additional incoherent coupling between the quantum dot and the cavity. DOI: 10.1103/PhysRevB.82.045306 PACS number͑s͒: 42.50.Pq, 85.35.Be Recent demonstrations of cavity quantum electrodynamics ͑CQED͒ with a single quantum dot ͑QD͒ coupled to a semiconductor microcavity show the great potential of this system for developing robust, scalable quantum information processing devices.1-4 However, unlike ultracold atoms, QDs constantly interact with their local environments and this interaction plays a significant role in CQED experiments with QDs. For example, several experiments have reported the observation of cavity emission even when the QD is far detuned ͑ϳ3-10 meV͒ from the cavity resonance, in contrast with atomic CQED experiments. This unexpected nonresonant QD-cavity coupling is observed both in photoluminescence, where the QD is excited by creating carriers above the band-gap of the GaAs surrounding the QD ͑Refs. 2, 5, and 6͒ and in the cavity luminescence under resonant excitation of the QD. 7,8 Recent theoretical investigations have attributed the off-resonant coupling to several different causes including pure dephasing, 9 phonon relaxation, 10 multiexciton complexes, 11 and charges surrounding the QD. 12In this paper, we experimentally study the process responsible for transferring photons between the QD and offresonant cavity mode, under resonant excitation of the QD or the cavity. We derive an analytical expression for the QD linewidth based on pure dephasing and coupling to the cavity, but find that experimentally obtained linewidths are larger than that predicted by the theory. We attribute this to an additional incoherent coupling mechanism between the QD and the cavity.When an off-resonant QD that is coupled to a cavity is coherently driven by a laser field, the QD is dressed by both the cavity and the laser field. In the absence of a driving laser, the dynamics of a coupled QD-cavity system is described by the Jaynes-Cummings HamiltonianHere, c and d are the cavity and the QD resonance frequency, respectively, is the lowering operator for the QD, a is the annihilation operator for the cavity photon and g is the coherent interaction strength between the QD and the cavity. The eigenfrequencies Ϯ of the coupled system are given bywhere 2 and 2␥ are the cavity energy decay rate and the QD spontaneous emission rate, respectively and ␦ is the QDcavity detuning d − c . When the coherent interaction strength g is greater than the decay rates and ␥, the system is in strong coupling regime, and the eigenstates of H JC are polaritons possessing the characteristics of both the cavity and the...

A theoretical model for the phonon-mediated off-resonant coupling between a quantum dot and a cavity, under resonant excitation of the quantum dot, is presented. We show that the coupling is caused by electron-phonon interaction in the quantum dot and is enhanced by the cavity. We analyze recently observed resonant quantum dot spectroscopic data by our theoretical model.

We investigate a singly-charged quantum dot under a strong optical driving field by probing the system with a weak optical field. When the driving field is detuned from the trion transition, the probe absorption spectrum is shifted from the trion resonance as a consequence of the dynamic Stark effect. Simultaneously, a gain sideband is created, resulting from the coherent energy transfer between the optical fields through the quantum dot nonlinearity. As the pump detuning is moved from red to blue, we map out the anticrossing of these two spectral lines. The optical Bloch equations for a stationary two-level atom can be used to describe the numerous spectral features seen in this nano solid state system. PACS numbers: 78.67.Hc,42.50.Hz,42.50.Gy Quantum dot (QD) nano-structures have been proposed for numerous quantum mechanical applications due to their customizable atom-like features [1]. One important application involves using these QDs as the building blocks for quantum logic devices [2]. An electron spin trapped inside a QD is a good candidate for a quantum bit (qubit) since it is known to have long relaxation [3] and decoherence times [4,5]. Recently, the electron spin coherence has been optically generated and controlled [5,6,7] in ensembles of QDs. The initialization of the electron spin state in a single QD has also been realized by optical cooling techniques [8,9].One important task is to understand and control the physical properties of a singly-charged QD in the strong optical field regime, i.e. the light-matter interaction strength is much larger than the transition linewidth, under both resonant and nonresonant excitation. Given the recent work on optically driven neutral quantum dots in strong fields [10,11] demonstrating many features similar to atomic systems, it is clear that a negatively charged quantum dot has similarities to a negative ion. However, the excited state of a dot is a many body structure comprised of two electrons and a hole. Interestingly, the results in this paper show that strong field excitation tuned near resonance in a negatively charged dot leads to changes in the absorption spectrum that are in excellent agreement with theory.In the time domain, the strong field interaction leads to the well-known Rabi oscillations [12,13,14,15]. In the frequency domain, it will introduce Rabi side bands in the absorption, and strikingly, the amplification of a probe beam. This phenomenon has been studied theoretically [16,17,18] and demonstrated experimentally in atomic systems [19,20]. Recently, these effects have also been observed in quantum dot and molecular systems [10,11,21,22]. The optical AC Stark effect has been seen by exciting a neutral QD with a detuned strong op- , respectively. However, the study of the singly-charged QDs in the strong field regime has been very limited at the single dot level [24]. In this letter, we investigate a singly-charged QD under a strong optical driving field with both on and off-resonant pumping. When the strong pump is on resonance with the t...

Equation (A26) from the paper should be corrected towhere ρ dos (ν) is the density of states of phonons at frequency ν and other parameters are explained in the original paper. The values of γ r used in the paper were based on the experimental results. Therefore, the error in Eq. (A26) does not affect any conclusions and results of the paper. The derivation of this expression follows Carmichael (Ref. 1, Chap. 1.3). Starting with the equations for correlation functions [(A24) and (A25)] from the paper, the summation over reservoir oscillators can be replaced with integration over the reservoir by introducing a density of states of phonons at a frequency ω as ρ dos (ω) [such that ρ dos (ω)dω gives the total number of oscillators, i.e., phonons with frequencies in the intervals ω and ω + dω], and transforming g j 23 → g 23 (ω). We note that, by such definition, ρ dos (ω) has a dimension of inverse frequency. This leads to the following expressions for the correlation functions (whereAfter the integration of these expressions (as in Ref. 1), the value of γ r given above can be extracted. As expected, γ r peaks when ν = , i.e., for phonon modes with frequencies equal to detuning between the quantum dot and the cavity mode. We note that, under our simplified assumption of phonon modes being lossless, γ r goes to infinity at such resonances. However, as stated above, we do not use this expression for any analysis in the paper and, instead, use experimental values of γ r . 1