Quantum logic gates with a two-level trapped ion in a high-finesse cavity beyond the Lamb–Dicke limit

Abstract

In the system with a two-level ion confined both in a linear trap and in a high-Q single-mode cavity, we present a simple scheme to realize the basic two-qubit logic gates such as the quantum phase gate (QPG), the SWAP gate and the controlled-NOT (CNOT) gate beyond the Lamb–Dicke (LD) limit. We realize the three kinds of two-qubit quantum phase gates, i.e. QPG operation involving the cavity mode as well as the vibrational mode of the trapped ion, QPG operation involving the internal states as well as the vibrational mode of the trapped ion and QPG operation involving the internal states of the trapped ion as well as the cavity mode. The controlled-NOT gate can be implemented from a QPG operation through a rotation of the second qubit before and after the QPG operation. We can also perform the SWAP gate operation involving the ionic internal states of the trapped ion and the two-mode bosonic basis. The logic gates involving the cavity mode as well as the vibrational mode of the trapped ion are insensitive to spontaneous emission, and the logic gates involving the internal states as well as the vibrational mode of the trapped ion are insensitive to the decay of the cavity, which is an important feature for the practical implementation of quantum computing. Neither the LD approximation nor the auxiliary atomic level is needed in our scheme. Experimental feasibility for achieving our scheme is also discussed.

Sub-Doppler cavity cooling beyond the Lamb-Dicke regime

“…Hence, the sum of these heating effects should raise the radial vibrational occupation number by ≈ 9 in 3 ms which causes an underestimation of the fitted cooperativity by 13%. Including these influencing factors, the fitted value of the cooperativity extrapolated to the LD regime is C = 0.38(3), within 2 σ range of the estimated cooperativity, 0.446 (21). The rest of the fitting parameters are within their respective estimations based on the independent measurement of the laser power and the sideband cooling efficiency.…”

“…(B4, B5, B6) for a birefringent cavity. The fitted value of the cooperativity extrapolated to the LD regime, C = 0.33 (3), is only 74(7)% of the estimated value, 0.446 (21). The discrepancy could be due to the additional heating along the ion radial direction such as recoil heating during the sideband cooling and the environmental heating caused by electronic noise.…”

“…However, the effective cooperativity is greatly reduced from this value due to the following factors: the reduced dipole matrix element for π-polarization (0.33), cavity birefringence (0.672 (13) at the midpoint between the modes) and branching ratio for S 1/2 ↔ P 1/2 transition (0.756( 12)) [39]. The combination of these independent parameters results in an effective cooperativity of C = 0.446 (21), valid for an ion in the LD regime.…”

“…The cavity enhances the interaction between the ion and a single photon, and enables efficient extraction of emitted photons. Proposed applications of trapped ion-cavity systems in QIP include quantum repeaters [13,14], entanglement of distant ions [15][16][17] and quantum logic gates [18][19][20][21]. To date, remarkable advancements have been made: single photon sources [11,22], single ion lasers [23] and ion-photon entanglement [12] have all been demonstrated with trapped ion-cavity setups.…”

Quantum logic gates with two-level trapped ions beyond Lamb–Dicke limit

“…[16] In fact, recently, several schemes have been proposed to implement the quantum computation and prepare entangled states with trapped ions outside the LD regime. [7,17,18] Recently, several schemes [19−21] have also been proposed for fast quantum computations in an ion trap, but the schemes of Refs. [19][20][21] require a number of laser-ion interactions.…”