Entanglement of Atomic Qubits Using an Optical Frequency Comb - eScholarship

PRL 104, 140501 (2010) Selected for a Viewpoint in Physics PHYSICAL REVIEW LETTERS week ending 9 APRIL 2010 Entanglement of Atomic Qubits Using an Optical Frequency Comb D. Hayes,* D. N. Matsukevich, P. Maunz, D. Hucul, Q. Quraishi, S. Olmschenk, W. Campbell, J. Mizrahi, C. Senko, and C. Monroe Joint Quantum Institute, Department of Physics, University of Maryland and National Institute of Standards and Technology, College Park, Maryland 20742 USA (Received 13 January 2010; published 5 April 2010) We demonstrate the use of an optical frequency comb to coherently control and entangle atomic qubits. A train of off-resonant ultrafast laser pulses is used to efficiently and coherently transfer population between electronic and vibrational states of trapped atomic ions and implement an entangling quantum logic gate with high fidelity. This technique can be extended to the high field regime where operations can be performed faster than the trap frequency. This general approach can be applied to more complex quantum systems, such as large collections of interacting atoms or molecules. DOI: 10.1103/PhysRevLett.104.140501 PACS numbers: 03.67.Bg, 32.80.Qk, 37.10.Rs, 37.10.Vz The optical frequency comb generated from an ultrafast laser pulse train has revolutionized optical frequency met- rology [1–4] and is now playing an important role in high resolution spectroscopy [5]. The spectral purity yet large bandwidth of optical frequency combs also provides a means for the precise control of generic quantum systems, with examples such as the quantum control of multilevel atomic systems [6,7], laser cooling of molecules or exotic atomic species [8,9], and quantum state engineering of spins in semiconductors [10,11] or rovibrational states in molecules [12,13]. The optical frequency comb may be- come a crucial component in the field of quantum infor- mation science, where complex multilevel quantum systems must be controlled with great precision [14]. In this Letter, we report the use of an optical frequency comb generated from an ultrafast mode-locked laser to efficiently control and faithfully entangle two trapped atomic ion qubits. The optical pulse train drives stimulated Raman transitions between hyperfine levels [15,16], ac- companied by qubit state-dependent momentum kicks [17]. The coherent accumulation of these pulses generates particular quantum gate operations that are controlled through the phase relationship between successive pulses. This precise spectral control of the process along with the large optical bandwidth required for bridging the qubit frequency splitting forms a simple method for controlling both the internal electronic and external motional states of trapped ion qubits, and may be extended to most atomic species. This same approach can be applied to control larger trapped ion crystals with more advanced pulse- shaping techniques, and can also be extended to a strong pulse regime where only a few high-power pulses are needed for fast quantum gate operations in trapped ions High fidelity qubit operations through Raman transitions are typically achieved by phase-locking frequency compo- nents separated by the energy difference of the qubit states. This is traditionally accomplished in a bottom-up type of approach where either two monochromatic lasers are phase locked or a single cw laser is modulated by an acousto- optic (AO) or an electro-optic (EO) modulator. However, the technical demands of phase-locked lasers and the lim- ited bandwidths of the modulators hinder their application to experiments. Here we exploit the large bandwidth of ultrafast laser pulses in a simple top-down approach toward bridging large frequency gaps and controlling complex atomic systems. By starting with the broad bandwidth of an ultrafast laser pulse, a spectral landscape can be sculpted by interference from sequential pulses, pulse shaping and frequency shifting. In this Letter, we start with a picosecond pulse and, through the application of many pulses, generate a frequency comb that drives Raman transitions by stimulating absorption from one comb tooth and stimulating emission into another comb tooth as de- picted in Fig. 1. Because this process only relies on the frequency difference between comb teeth, their absolute position is irrelevant and the carrier-envelope phase does not need to be locked. As an example of how this new technique promises to ease experimental complexities, metastable-state qubits separated in frequency by a tera- hertz have been controlled using cw lasers phase-locked through a frequency comb [20], but might be controlled directly with a 100 fs Ti:sapphire pulsed laser. At a fixed point in space, an idealized train of laser pulses has a time-dependent electric field that can be written as N X fðt nTÞe i! c t ; EðtÞ ¼ n¼1 where fðtÞ is the pulse envelope, T is the time between successive pulses (repetition rate R ¼ 1=T), N is the number of pulses in the train and ! c is the carrier fre- quency of the pulse. For simplicity, any pulse-to-pulse optical phase shift is ignored since the offset frequency in the comb is unimportant. The Fourier transform of Eq. (1) defines a frequency comb characterized by an envelope fð!Þ F½fðtÞ centered around the optical fre- quency ! c and teeth separated by R whose individual O 2010 The American Physical Society