Physica E 35 (2006) 251–256 Preparing, manipulating, and measuring quantum states on a chip J.R. Petta a,Ã , A.C. Johnson a , J.M. Taylor a , E.A. Laird a , A. Yacoby b , M.D. Lukin a , C.M. Marcus a , M.P. Hanson c , A.C. Gossard c a Department of Physics, Harvard University, Cambridge, MA 02138, USA b Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel c Materials Department, University of California, Santa Barbara, CA 93106, USA Available online 3 November 2006 Abstract We use gate voltage control of the exchange interaction to prepare, manipulate, and measure two-electron spin states in a GaAs double quantum dot. By placing two electrons in a single dot at low temperatures we prepare the system in a spin singlet state. The spin singlet is spatially separated by transferring an electron to an adjacent dot. The spatially separated spin singlet state dephases in 10 ns due to the contact hyperfine interaction with the GaAs host nuclei. To combat the hyperfine dephasing, we develop quantum control techniques based on fast electrical control of the exchange interaction. We demonstrate coherent spin-state rotations in a singlet–triplet qubit and harness the coherent rotations to implement a singlet–triplet spin echo refocusing pulse sequence. The singlet–triplet spin echo extends the spin coherence time to 1:2 ms. r 2006 Elsevier B.V. All rights reserved. PACS: 03.67.Mn; 72.25.Rb; 85.35.Gv Keywords: Spin qubit; Coherent manipulation; Spin echo 1. Introduction The ability to prepare, manipulate, and measure quantum mechanical coherence has traditionally been confined to the fields of atomic, molecular, and optical physics [1,2]. Recent advances in experimental condensed matter physics have made it possible to demonstrate comparable quantum control in artificially structured solid state systems [3–5]. In this paper we demonstrate how GaAs double quantum dots can be used to prepare, manipulate, and measure quantum states based on the spin degree of freedom of two electrons [6]. These devices form an elementary quantum bit. At the same time, they are a sensitive probe of the environment and can be used to study the basic physics that leads to spin relaxation and spin dephasing [6,7]. Gate defined GaAs/AlGaAs nanostructures have been one of the workhorses of mesoscopic physics [8,9]. It has recently become possible to isolate a single electron in a gate defined GaAs quantum dot [10]. This work was quickly extended to include more complicated double and triple quantum dots [11–13]. In these systems, electrons can be moved from one quantum dot to another simply by adjusting electrostatic potentials using DC gate voltages. Manipulating these gate voltages using high-speed techni- ques has enabled coherent manipulation of the charge degree of freedom [14]. In this paper, we will describe how fast gate voltage control can be used to manipulate two- electron spins that are coupled together by a tunable exchange interaction [6,7,15]. 2. Experimental details Gate defined double quantum dots are fabricated from a GaAs=Al 0:3 Ga 0:7 As heterostructure grown by molecular beam epitaxy (Fig. 1). The two-dimensional electron gas (2DEG) has an electron density of 2  10 11 cm 2 and a mobility of 2  10 5 cm 2 =V s. Electrical contact to the 2DEG is made by depositing AuGe wirebonding pads, ARTICLE IN PRESS www.elsevier.com/locate/physe 1386-9477/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2006.08.020 Ã Corresponding author. Tel.: +609 258 1173. E-mail address: petta@princeton.edu (J.R. Petta).