Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms

Abstract

Accurate control of a quantum system is a fundamental requirement in many areas of modern science ranging from quantum information processing to high-precision measurements. A significantly important goal in quantum control is preparing a desired state as fast as possible, with sufficiently high fidelity allowed by available resources and experimental constraints. Stimulated Raman adiabatic passage (STIRAP) is a robust way to realize high-fidelity state transfer but it requires a sufficiently long operation time to satisfy the adiabatic criteria. Here we theoretically propose and then experimentally demonstrate a shortcut-to-adiabatic protocol to speed-up the STIRAP. By modifying the shapes of the Raman pulses, we experimentally realize a fast and high-fidelity stimulated Raman shortcut-to-adiabatic passage that is robust against control parameter variations. The all-optical, robust and fast protocol demonstrated here provides an efficient and practical way to control quantum systems.

Introduction

Coherent control of the quantum state is an essential task in various areas of physics, such as high-precision measurement1,2, coherent manipulation of atom and molecular systems3,4, and quantum information5,6. In most applications, the basic requirement of coherent control is to reach a given target state with high fidelity as fast as possible. Many schemes have been developed for this purpose, including the adiabatic passage technique, which drives the system along its eigenstate7,8,9,10. One of attractive property of this technique is that the resulting evolution is robust against control parameter variations when the adiabatic condition is fully satisfied. However, the adiabatic passage techniques such as the two-level adiabatic passage10, three-level stimulated Raman adiabatic passage (STIRAP)11 and their variants are time consuming to realize, which limits their applications in some fast dephasing quantum systems. To overcome this shortcoming, several protocols within the framework of the so-called ‘shortcut-to-adiabaticity’12 have been proposed to speed-up the ‘slow’ adiabatic passage: for instance, counter-diabatic driving (equivalently, the transitionless quantum algorithm)13,14,15,16. Very recently, the acceleration of the adiabatic passage has been demonstrated experimentally in two-level systems: an energy-level anticrossing for a Bose–Einstein condensate loaded into an accelerated optical lattice17and the electron spin of a single nitrogen-vacancy centre in diamond18.

The STIRAP based on the two-photon stimulated Raman transition has several advantages. First, lasers can be focused on a single site in an optical lattice or on a single ion in a linear ion trap, which guarantees individual addressability19,20,21. Second, the STIRAP can couple two states that cannot be directly coupled, such as transferring population between two atomic states with the same parity (which cannot be directly coupled via electric dipole transition)22, or transferring the atomic state to the molecular state3. Furthermore, with large single-photon detuning, double coherent adiabatic passages exist23,24,25, which guarantees the capacity for state transfer between arbitrary states25,26,27. Interestingly, several theoretical protocols have been proposed to speed-up the STIRAP by adding an additional microwave field in various atom and molecular systems28,29,30,31. However, the transfer fidelity will depend on the phase differences among the microwave field, the Stokes and pumping laser pulses for the STIRAP, which are difficult to lock. Furthermore, the combination of the microwave field and Raman lasers makes it difficult to feature the individual addressability of the operation. Therefore, speeding up the STIRAP has not yet been experimentally demonstrated.

Motivated by the goal of a robust, fast, addressable, arbitrary state transfer protocol, we propose a feasible scheme to speed-up STIRAP by modifying the shapes of two Raman pulses. We utilize the counter-diabatic driving along with unitary transformation, one of the shortcut techniques to realize adiabatic passages. We then experimentally demonstrate the proposed stimulated Raman shortcut-to-adiabatic passage (STIRSAP) protocol in a large single-photon detuning three-level Λ system with a cold atomic ensemble. The passage’s robustness against parameter variation is confirmed in our experiments. Fast, robust, individually addressable and arbitrarily transferable between states, the quantum state control protocol demonstrated here is useful for practical applications.

Results

STIRAP and STIRSAP protocols

We consider a cold 87Rb atom ensemble (see the Methods section) whose internal energy states |1〉 (|2〉) and |3〉 are coupled by pumping pulse ΩP(t) (Stokes pulse ΩS(t)), as shown in Fig. 1a. Two ground states |F=1, mF=0〉=|1〉; |F=2, mF=0〉=|2〉 and one excited state 52P3/2 (=|3〉) are selected as a typical three-level Λ system. Under the conditions of rotating-wave approximation and two-photon detuning δ=0, the interaction Hamiltonian of the system in the basis of {|1〉, |2〉, |3〉} is given as

Figure 1: Experimental scheme.

(a) Experimental set-up. The laser-atom coupling scheme of the three-level Λ system is shown in the upper panel. Two ground states |F=1, mF=0〉=|1〉; and |F=2, mF=0〉=|2〉, and one excited state 52P3/2 (=|3〉)of 87Rb are selected as a typical three-level Λ system. The states |1〉, (|2〉) and |3〉 are coupled by pumping pulse ΩP(t) (Stokes pulse ΩS(t)). The single-photon detuning Δ between the Raman lasers and the excited state 52P3/2 is about 2.5 GHz. A magnetic field Bz is used to split the Zeeman sublevels. Two Raman laser fields (pumping ΩP(t) and Stokes ΩS(t)) with phase-locked are combined by a beam splitter (BS) and then send to interact with the cold atoms. The shapes of the Raman lasers are modulated by two AOMs driven by a radio source (RS). (b) The original Raman laser pulses in the usual STIRAP are two partially overlapping Gaussian shapes. (c) Modified Raman laser pulses for STIRSAP obtained from equation (3).