We show that resonance fluorescence, i.e. the resonant emission of a coherently driven two-level system, can be realized with a semiconductor quantum dot. The dot is embedded in a planar optical micro-cavity and excited in a wave-guide mode so as to discriminate its emission from residual laser scattering. The transition from the weak to the strong excitation regime is characterized by the emergence of oscillations in the first-order correlation function of the fluorescence, g(τ ), as measured by interferometry. The measurements correspond to a Mollow triplet with a Rabi splitting of up to 13.3 µeV. Second-order-correlation measurements further confirm non-classical light emission. [3,4,5,6,7], as well as photon anti-bunching [8], and were previously only observable in isolated atoms or ions. In addition, QDs can be readily integrated into optical micro-cavities making them attractive for a number of applications, particularly quantum information processing and high efficiency light sources. For example, QDs could be used to realize deterministic solid-state single photon sources [9,10,11] and qubit-photon interfaces [12]. Advances in high-Q cavities have shown that not only can the spontaneous emission rate be dramatically increased by the Purcell effect [13,14], but emission can be reversed in the strong coupling regime [15,16,17]. Despite these efforts, however, quantum dot-based cavity quantum electrodynamics (QED) lacks an ingredient essential to the success of atomic cavity QED, namely the ability to truly resonantly manipulate the two-level system [9,10,11]. Current approaches can at best populate the dot in one of its excited states, which subsequently relaxes in some way to the emitting ground state. This incoherent relaxation has been addressed theoretically [18,19], and experimentally [20] but direct resonant excitation and collection in the ground state has so far not been reported as it is very challenging to differentiate the resonance fluorescence from same-frequency laser scattering off defects, contaminants, etc. In quantum dots without cavities, coherent manipulation of ground-state excitons has nonetheless been achieved with a number of techniques including differential transmission [6], differential * Electronic address: shih@physics.utexas.edu reflectivity [21], four-wave mixing [22], photodiode spectroscopy [7], and Stark-shift modulation absorption spectroscopy [23]. However, none of these is able to collect and use the actual photon emission which limits their use in many potential applications of QDs. This report presents the first measurement of resonance fluorescence in a single self-assembled quantum dot. Described by Mollow in 1969 [24], the resonant emission of a two-state quantum system under strong coherent excitation is distinguished by an oscillatory first-order correlation function, g(τ ), that we observe with interferometry. We use a planar optical micro-cavity to guide the excitation laser between the cavity mirrors and simultaneously enhance the single photon emission in th...

Using photoluminescence spectroscopy, we have investigated the nature of Rabi oscillation damping during active manipulation of excitonic qubits in self-assembled quantum dots. Rabi oscillations were recorded by varying the pulse amplitude for fixed pulse durations between 4 ps and 10 ps. Up to 5 periods are visible, making it possible to quantify the excitation dependent damping. We find that this damping is more pronounced for shorter pulse widths and show that its origin is the non-resonant excitation of carriers in the wetting layer, most likely involving bound-to-continuum and continuum-to-bound transitions. Hz, 78.47.+p, 78.55.Cr The current topic of quantum computation presents a wide range of challenges to physical science [1], particularly the search for candidates for solid-state quantum bits (qubits). Semiconductor quantum dots (QDs) are attractive because they possess energy structures and coherent optical properties similar to, and dipole moments larger than, those of atoms [2,3]. Efforts in the past few years have led to successful observations of Rabi oscillations (ROs) of excitonic states [4][5][6][7][8][9], the hallmark for active manipulation of qubits in QDs. However, all found that ROs damped out very quickly when the external field is increased. Because QDs contain a macroscopic number of atoms, this strong decoherence process must be due to unwanted coupling to other degrees of freedom.Identification of the underlying mechanism is difficult precisely because of this macroscopic nature. Yet such understanding plays the most crucial role in future development of quantum information technology in semiconductors. Through manipulations of high quality factor excitonic qubits in InGaAs QDs, we have studied the underlying mechanism for decoherence processes during active manipulation. More specifically, we have found that this strong decoherence process is manifested through indirect excitations of carriers in the wetting layer whose composition is highly fluctuating.We study In 0.5 Ga 0.5 As self-assembled QD (SAQD) samples grown by molecular beam epitaxy (MBE). The details of growth processes are given in [10]. These QDs are 3 3 embedded in a GaAs matrix with a wetting layer of roughly 5 monolayers thickness. The dots have an average lateral size, height, and dot-to-dot distance of 20-40 nm, 4.5 nm and 100 nm, respectively, characterized using cross-sectional scanning tunnelling microscopy. There are three excitonic levels involved: The exciton vacuum (labelled as |0Ú) when there is no electron-hole pair present, the single exciton ground state, (labelled as |2Ú), and the first excited state of the exciton (labelled as |1Ú). The qubit is based on the two level system formed by |0Ú and |1Ú. The exciton ground state |2Ú is a spectator state used to monitor the population of state |1Ú. This is possible because |1Ú decays nonradiatively to |2Ú long before it can radiatively decay to |0Ú. The state |1Ú then decays radiatively to |0Ú and is detected as the photoluminescence (PL) signal as summariz...

We study the behavior of an open quantum system, with an N-dimensional space of states, whose density matrix evolves according to a nonunitary map defined in two steps: A unitary step, where the system evolves with an evolution operator obtained by quantizing a classically chaotic map (baker's map and Harper's map are the two examples we consider). A nonunitary step where the evolution operator for the density matrix mimics the effect of diffusion in the semiclassical (large N) limit. The process of decoherence and the transition from quantum to classical behavior are analyzed in detail by means of numerical and analytic tools. The existence of a regime where the entropy grows with a rate that is independent of the strength of the diffusion coefficient is demonstrated. The nature of the processes that determine the production of entropy is analyzed.

We perform quantum interference experiments on a single self-assembled semiconductor quantum dot. The presence or absence of a single exciton in the dot provides a qubit that we control with femtosecond time resolution. We combine a set of quantum operations to realize the singlequbit Deutsch-Jozsa algorithm. The results show the feasibility of single qubit quantum logic in a semiconductor quantum dot using ultrafast optical control.PACS numbers: 78.55. Cr,03.67.Lx Time-resolved optical spectroscopy in semiconductor quantum dots has recently progressed toward the full quantum control of excitons trapped inside a single dot. 1,2,3,4 These advances have stimulated proposals to use excitons in quantum dots as quantum bits 5,6,7 for implementation of quantum computing. Very recently, the ability to operate a two-qubit gate using exciton and biexciton states was demonstrated in a single quantum dot. 8 These achievements represent a step toward an alloptical implementation of quantum computing using excitonic qubits. The first algorithm that comes to mind in order to check the feasibility of quantum computation in this context is the Deutsch-Jozsa (DJ) algorithm. 9 This algorithm is one of the simplest quantum algorithms that provides an exponential speed-up with respect to classical algorithms. As such, it has been extensively studied and has been used in experimental demonstrations of simple quantum computation in a variety of systems. 10,11,12 In this Rapid Communication we report the experimental realization of the DJ algorithm for a single qubit using an optimized version of the algorithm 13 .The Deutsch problem 9 involves global properties of binary functions on a subset of the natural numbers. Given a natural number N , we can define a set called X N with all the natural numbers that can be represented with N bits. A binary function f : X N → {0, 1} is called balanced if it returns 0 for exactly half of the elements of X N and 1 for the other half. Given a function that is either balanced or constant, the Deutsch problem consists of finding out which type it is. A general classical algorithm requires evaluating the function on more than half of the elements, requiring at least 2 N −1 + 1 evaluations. This causes the classical run time to grow exponentially with the input size. The Deutsch-Jozsa algorithm provides a way to solve the Deutsch problem on a quantum computer using a quantum subroutine that evaluates f . The problem and its solution provide an example of Oracle-based quantum computation. 14,15 It is assumed that a quantum subroutine or Oracle contains the information about the unknown function. The algorithm gives a recipe on how to prepare (encoding) and read out (decoding) the qubit in an efficient way. In an experimental demonstration, we have not only to implement the algorithm (encoding and decoding operations), but we also have to build the Oracle. The specific structure of the Oracle, encoding and decoding is not unique and several versions can be found in the literature. 9,13,16,17 . The on...

We show how to represent the state and the evolution of a quantum computer (or any system with an N -dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary N , is defined in a phase space grid of 2N × 2N points. We compute such Wigner function for states which are relevant for quantum computation. Finally, we discuss properties of quantum algorithms in phase space and present the phase space representation of Grover's quantum search algorithm.PACS numbers: 02.70. Rw, 03.65.Bz, 89.80.+h Wigner functions [1] provide a simple representation of the quantum state of a continuous system in phase space. This is important when analyzing issues related with the classical limit of quantum mechanics [2]. In this letter we study a useful generalization of the Wigner function to systems with N -dimensional Hilbert spaces. We use this Wigner function to obtain, for the first time, a phase space representation of both the states and the temporal evolution of a quantum computer. What are the potential advantages of a phase space representation of a quantum computer? It is clear that quantum algorithms can be thought of as quantum maps operating in a finite state space and are therefore amenable to this representation. Whether it will be useful or not will depend on properties of the algorithm. Specifically, algorithms become interesting in the large N limit (i.e. when operating on many qubits). For a quantum map this is the semiclassical limit where many new regularities arise in connection with its classical behaviour in phase space. Thus unraveling these regularities, when they exist, becomes an important issue which can be naturally accomplished in a phase space representation. Moreover, this phase space approach may allow one to establish contact between the vast literature on quantum maps (dealing with their construction, semiclassical properties, etc) and that of quantum algorithms providing hints to develop new algorithms. As a first application of these ideas we show how Grover's search algorithm [3] can be represented in phase space and interpreted as a simple quantum map.For a particle in 1 dimension the Wigner function, [1]