Generation of any superposition of Dicke state of excitons in coupled quantum dots

We present a scheme to generate arbitrary superposition of the Dicke states of excitons in optically driven quantum dots. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on Dicke state. It is shown that N laser pulses are needed to generate arbitrary superposition of the Dicke states of N quantum dots. PACS number(s): 03.67.-a, 03.67.Hk. Quantum entanglement has been intensely studied, due to its poential applications in quantum communication and information processing[?] such as quantum teleportation[2], superdense coding[3], quantum key distribution[4] and telecloning[5]. One other area where entangled quantum state may have a significant impact is that of the improvement of frequency standard[6, 7]. Key to improvement of frequency standard beyond the short noise limit is the establishment of a entangled state of a collection of N two level atoms. Initial theoretical investigation examined the use of spin squeezed state[6, 7], which has been extensively studied[8] in recent years. It has also been shown that, in the absence of decoherence, GHZ state of N the may be used in high precision spectroscopy to measure the transition frequency to an uncertainty of N−1[9, 10]. When the decoherence is present, the use of the maximally entangled state does not provide higher resolution as compared to using independent particle and the best sensitivity is achieved when the particles are initially prepared in highly symmetric but only partially entangled states[10], which is a superposition of the Dicke states. A number of experimental protocols for generation of GHZ state of N qubits and spin squeezed state have been proposed, including the Cavity QED[11], trapped ion system[12] and Bose-Einstein condensates[8]. In experiment, GHZ state of three or four qubits has been observed[13]. Recently, it has been shown that there exist two inequivalent classes of three qubit entangled state under local operation assisted by classical communication, namely GHZ state |GHZ >= 1 √ 2 (|111 > +|000 >) and W state |GHZ >= 1 √ 3 (|100 > +|010 > +|001 >)[14]. A scheme has also been proposed for generating W entangled state of three or four qubits[15]. In this paper, we present a scheme to generate arbitrary superposition of the Dicke states of N atoms, which includes GHZ and W state of N qubits, spin squeezed state and entangled atomic 1 state proposed in Ref[10]. Our scheme is based on optical driven quantum dots. Recent advance in semiconductor nanostructure fabrication and measurement suggest that optically generated electron-hole pairs (exciton) in semiconductor quantum dot represent ideal candidate for achieving coherence wave function control on the nanometer and femtosecond scales and implementing a large scale quantum computation[16]. Recently, optically driven quantum dot has been used to prepare maximally entangled Bell and GHZ state[17] and implement quantum teleportation[18]. In this paper, we present a scheme to generate arbitrary superposition of the Dicke states of excitons in optically driven quantum dots. This proposal is based on a sequence of laser pulses, which are tuned appropriately to control transitions on Dicke state. It is shown that only one laser pulses are needed to generate W states of N quantum dots. The schematic requirement are realizable in current experiment employing ultrafast optical spectroscopy of quantum dots. In order to describe our scheme, we consider a system of N identical and equispaced quantum dots containing no net charge that are radiated by long-wavelength classical light. In the frame of the rotating wave approximation, the formation of single excitons within the individual quantum dots and their interdot hopping are described by the Hamiltonian[17, 18] H = ∆ω + ge J+ + ge J− +W (J 2 − J z ) (1) where J+ = N