Coherent control to prepare an InAs quantum dot for spin-photon entanglement.

We optically generated an electronic state in a single InAs/GaAs self-assembled quantum dot that is a precursor to the deterministic entanglement of the spin of the electron with an emitted photon in the proposal of W. Yao, R.-B. Liu, and L. J. Sham [Phys. Rev. Lett. 95, 030504 (2005). A superposition state is prepared by optical pumping to a pure state followed by an initial pulse. By modulating the subsequent pulse arrival times and precisely controlling them using interferometric measurement of path length differences, we are able to implement a coherent control technique to selectively drive exactly one of the two components of the superposition to the ground state. This optical transition contingent on spin was driven with the same broadband pulses that created the superposition through the use of a two pulse coherent control sequence. A final pulse affords measurement of the coherence of this "preentangled" state.

Demonstration of quantum entanglement between a single electron spin confined to an InAs quantum dot and a photon.

The electron spin state of a singly charged semiconductor quantum dot has been shown to form a suitable single qubit for quantum computing architectures with fast gate times. A key challenge in realizing a useful quantum dot quantum computing architecture lies in demonstrating the ability to scale the system to many qubits. In this Letter, we report an all optical experimental demonstration of quantum entanglement between a single electron spin confined to a single charged semiconductor quantum dot and the polarization state of a photon spontaneously emitted from the quantum dot's excited state. We obtain a lower bound on the fidelity of entanglement of 0.59±0.04, which is 84% of the maximum achievable given the timing resolution of available single photon detectors. In future applications, such as measurement-based spin-spin entanglement which does not require sub-nanosecond timing resolution, we estimate that this system would enable near ideal performance. The inferred (usable) entanglement generation rate is 3×10(3) s(-1). This spin-photon entanglement is the first step to a scalable quantum dot quantum computing architecture relying on photon (flying) qubits to mediate entanglement between distant nodes of a quantum dot network.

Fast spin rotations by optically controlled geometric phases in a charge-tunable InAs quantum dot.

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.

Single charged quantum dot in a strong optical field: absorption, gain, and the ac-Stark effect.

We investigate a singly charged quantum dot under a strong optical driving field by probing the system with a weak optical field. We observe all critical features predicted by Mollow for a strongly driven two-level atomic system in this solid state nanostructure, such as absorption, the ac-Stark effect, and optical gain. Our results demonstrate that even at high optical field strengths the electron in a single quantum dot with its dressed ground state and trion state behaves as a well-isolated two-level quantum system.

Fast spin state initialization in a singly charged InAs-GaAs quantum dot by optical cooling.

Quantum computation requires a continuous supply of rapidly initialized qubits for quantum error correction. Here, we demonstrate fast spin state initialization with near unity efficiency in a singly charged quantum dot by optically cooling an electron spin. The electron spin is successfully cooled from 5 to 0.06 K at a magnetic field of 0.88 T applied in Voigt geometry. The spin cooling rate is of order 10(9) s-1, which is set by the spontaneous decay rate of the excited state.

Selective optical control of electron spin coherence in singly charged GaAs-Al0.3Ga0.7As quantum dots.

Coherent transient excitation of the spin ground states in singly charged quantum dots creates optically coupled and decoupled states of the electron spin. We demonstrate selective excitation from the spin ground states to the trion state through phase sensitive control of the spin coherence via these three states, leading to partial rotations of the spin vector. This progress lays the ground work for achieving complete ultrafast spin rotations.

Fast initialization of the spin state of an electron in a quantum dot in the Voigt configuration.

We consider the initialization of the spin state of a single electron trapped in a self-assembled quantum dot via optical pumping of a trion level. We show that with a magnetic field applied perpendicular to the growth direction of the dot, a near-unity fidelity can be obtained in a time equal to a few times the inverse of the spin-conserving trion relaxation rate. This method is several orders of magnitude faster than with the field aligned parallel, since this configuration must rely on a slow hole spin-flip mechanism. This increase in speed does result in a limit on the maximum obtainable fidelity, but we show that for InAs dots, the error is very small.

Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot.

We demonstrate single qubit density matrix tomography in a single semiconductor quantum dot system through consecutive phase sensitive rotations of the qubit via ultrafast coherent optical excitations. The result is important for quantifying gate operations in quantum information processing in the quantum dot systems as well as demonstrating consecutive arbitrary qubit rotations.

Stimulated and spontaneous optical generation of electron spin coherence in charged GaAs quantum dots.

We report on the coherent optical excitation of electron spin polarization in the ground state of charged GaAs quantum dots via an intermediate charged exciton (trion) state. Coherent optical fields are used for the creation and detection of the Raman spin coherence between the spin ground states of the charged quantum dot. The measured spin decoherence time, which is likely limited by the nature of the spin ensemble, approaches 10 ns at zero field. We also show that the Raman spin coherence in the quantum beats is caused not only by the usual stimulated Raman interaction but also by simultaneous spontaneous radiative decay of either excited trion state to a coherent combination of the two spin states.

Optical RKKY interaction between charged semiconductor quantum dots.

We show how a spin interaction between electrons localized in neighboring quantum dots can be induced and controlled optically. The coupling is generated via virtual excitation of delocalized excitons and provides an efficient coherent control of the spins. This quantum manipulation can be realized in the adiabatic limit and is robust against decoherence by spontaneous emission. Applications to the realization of quantum gates, scalable quantum computers, and to the control of magnetization in an array of charged dots are proposed.

Raman coherence beats from entangled polarization eigenstates in InAs quantum dots.

The homodyne-detected transient four-wave-mixing response of InAs/GaAs self-assembled quantum dots shows temporal oscillations of the optically induced Raman coherence arising from two entangled polarization eigenstates of the exciton. The phase sensitive nature of the homodyne detection enables us to follow the time evolution of the nonradiative quantum coherence between the polarization states, providing a measurement of the fine-structure splitting in the dots, which is much less than the inhomogeneous broadening, and the corresponding decoherence rate of the entangled state.

Biexciton quantum coherence in a single quantum dot.

Nondegenerate (two-wavelength) two-photon absorption using coherent optical fields is used to show that there are two different quantum mechanical pathways leading to formation of the biexciton in a single quantum dot. Of specific importance to quantum information applications is the resulting coherent dynamics between the ground state and the biexciton from the pathway involving only optically induced exciton/biexciton quantum coherence. The data provide a direct measure of the biexciton decoherence rate which is equivalent to the decoherence of the Bell state in this system, as well as other critical optical parameters.

Rabi oscillations of excitons in single quantum dots.

Transient nonlinear optical spectroscopy, performed on excitons confined to single GaAs quantum dots, shows oscillations that are analogous to Rabi oscillations in two-level atomic systems. This demonstration corresponds to a one-qubit rotation in a single quantum dot which is important for proposals using quantum dot excitons for quantum computing. The dipole moment inferred from the data is consistent with that directly obtained from linear absorption studies. The measurement extends the artificial atom model of quantum dot excitonic transitions into the strong-field limit, and makes possible full coherent optical control of the quantum state of single excitons using optical pi pulses.

Mg2+ binding to alkaline phosphatase correlates with slow changes in protein lability.

The in vitro reactivation of unfolded Escherichia coli alkaline phosphatase (AP) in the presence of the two natively bound metals Zn2+ and Mg2+ produces two protein species, characterized by different guanidine hydrochloride denaturation kinetics. The high-lability AP form slowly converts to the low-lability form in a first-order reaction with a characteristic lifetime (inverse rate constant) of approximately 300 h at pH 8.0 and 25 degrees C. Addition of Zn2+ and Mg2+ ligands to (folded) apo-AP also produces two protein species, with denaturation kinetics and a long conversion lifetime similar to those found in refolding AP. In contrast, adding Zn2+ alone to apo-AP produces only the high-lability species with no subsequent structural change, suggesting that Mg2+ binding is the event which is responsible for the production of the low-lability AP. The rate of conversion from high- to low-lability AP was found to be linearly dependent on Mg2+ concentration, indicating that Mg2+ binding is rate limiting for this reaction. Experiments where either Zn2+ or Mg2+ was added first, with the second metal added later, show that Mg2+ binding is slowed by the prior presence of bound Zn2+. Mg2+ binding to Zn-AP also slightly increases the enzymatic activity; however, the extent of formation of the low-lability species is related to the square of the Mg2+-induced activity increase. Thus the binding of two Mg2+ to AP produces the dramatic reduction in the rate of denaturation that characterizes the low-lability species. The data suggest the possibility of long distance intersubunit interactions and a role for Mg2+ in providing "kinetic stability" for AP.

Near-field coherent spectroscopy and microscopy of a quantum dot system.

We combined coherent nonlinear optical spectroscopy with nano-electron volt energy resolution and low-temperature near-field microscopy with subwavelength resolution (

Differences in the pathways for unfolding and hydrogen exchange among mutants of Escherichia coli alkaline phosphatase.

Our initial studies of hydrogen-deuterium (H-D) exchange of tryptophan 109 in Escherichia coli alkaline phosphatase (AP) suggested that significant local unfolding of the protein might occur to allow for the exchange reaction, which is very slow at room temperature (Fischer et al., Biochemistry 39 (2000) 1455-1461). In order to investigate whether the partial unfolding and/or 'breathing' motions leading to H-D exchange were part of the unfolding pathway of the protein we prepared a series of mutants, designed to produce cavities around the exchanging residue, and compared their rates of H-D exchange to their lability (rate of inactivation) in guanidine hydrochloride (Gd:HCl). The complex unfolding kinetics of the mutants in the presence of Gd:HCl showed several components with rates that differed substantially among these proteins, but none of the rates of denaturation induced with Gd:HCl was consistently correlated with the H-D exchange rates. We conclude that the partial opening of the AP structure during the H-D exchange of tryptophan 109, although very slow, is not a rate determining step in the unfolding of this protein.

Hydrogen exchange at the core of Escherichia coli alkaline phosphatase studied by room-temperature tryptophan phosphorescence.

The room-temperature tryptophan (Trp) phosphorescence lifetime is sensitive to details of the local environment and has been shown to increase significantly in some proteins following H-D exchange. Careful analysis of the phosphorescence lifetime distribution of Trp 109 in Escherichia coli alkaline phosphatase (AP) in solution as a function of time during the H-D exchange shows that this process corresponds to a two-state reaction resulting from the deuteration of a single, specific hydrogen in the core of the protein. The absence of a pH dependence of the exchange rate suggests that the exchange is not an EX2 process, and therefore, a certain degree of unfolding is required for exchange to occur. This discovery opens up the use of phosphorescence-detected hydrogen exchange as a sensitive tool for monitoring the local susceptibility and activation energy for exchange in proteins having a phosphorescent Trp and, for example, for studying the effects of local mutations upon that susceptibility.

Proline isomerization is unlikely to be the cause of slow annealing and reactivation during the folding of alkaline phosphatase.

The in vitro folding of Escherichia coli alkaline phosphatase (AP) from the guanidine hydrochloride (GdnHCl) denatured state is characterized by a significant slow phase in the post activational recovery of native protein lability (probed by the susceptibility to GdnHCl denaturation and occurring on the time scale of days) as well as a slow phase in the recovery of activity (on the time scale of minutes). Slow folding events have often been attributed to cis-trans isomerizations of X-Pro peptide bonds, a plausible explanation for AP, which contains 21 prolines per subunit. To investigate the role of proline isomerization in the two measures of refolding mentioned above, we have performed "double-jump" GdnHCl denaturation/renaturation experiments, with a third jump, where the rate of unfolding of refolded protein upon exposure to denaturant was added to assess the rate of change of lability. Our measurements of the time evolution of both the lability and the reactivation of refolded AP as a function of denaturation time show that proline isomerization is unlikely to be the cause of either of these slow events in the refolding of AP. The conclusions are further confirmed by the absence of proline isomerization effects when AP is refolded in the presence of human and periplasmic E. coli peptidyl-prolyl isomerase.

Using census data to investigate the causes of the ecological fallacy.

"The authors show how data from the 2% Sample of Anonymised Records (SAR) can be combined with data from the Small Area Statistics (SAS) database to investigate the causes of the ecological fallacy in an Enumeration District (ED) level analysis. A range of census variables are examined in three ¿SAR districts'...in England. Results of comparable analyses from the 1986 Australian census are also given. The ecological fallacy arises when results from an analysis based on area-level aggregate statistics are incorrectly assumed to apply at the individual level.... A methodology is introduced which allows aggregate-level statistics to be adjusted by using individual-level information on those variables that explain much of the within-area homogeneity."

Near-field scanning optical microscopy of single molecules by femtosecond two-photon excitation.

We present a demonstration of near-field scanning optical microscopy of single molecules based on ultrafast two-photon-induced fluorescence. Measurements were performed by use of 100-fs pulses at 800 nm from a Ti:sapphire laser to excite the two-photon transition in Rhodamine B molecules. Although near-field probes are normally metal coated to achieve superresolution, we used uncoated tips to achieve sufficiently high optical powers to generate acceptable fluorescence emission rates. Images of single molecules demonstrate a resolution of ~175nm(< lambda/4) on a topographically smooth surface, which surpasses the apparent lambda/2 resolution limit for uncoated tips operating in the linear response regime.