ОПТИКА И СПЕКТРОСКОПИЯ, 2011, том 111, № 4, с. 575-581
ПЕРЕПУТАННЫЕ СОСТОЯНИЯ КВАНТОВЫХ СИСТЕМ ^^^^^^ ИЗ ДВУХ И БОЛЕЕ ЧАСТЕЙ
УДК 535.14
ENTANGLEMENT OF TWO GROUND STATE NEUTRAL ATOMS USING
RYDBERG BLOCKADE
© 2011 Y. Miroshnychenko***, A. Browaeys**, C. Evellin**, A. Gaёtan**, T. Wilk**, J. Wolter**, P. Grangier**, A. Chotia***, D. Comparat***, P. Pillet***, and M. Viteau***
*QUANTOP — Danish National Research Foundation's Centerfor Quantum Optics, Department of Physics and Astronomy
University of Aarhus, Denmark **Laboratoire Charles Fabry de l'Institut d'optique, CNRS, Univ, Paris-sud, France ***Laboratoire Aimé Cotton,CNRS, Univ, Paris-sud, France e-mail: miroshny@phys.au.dk Received April 18, 2011
Abstract—We report on our recent progress in trapping and manipulation of internal states of single neutral rubidium atoms in optical tweezers. We demonstrate the creation of an entangled state between two ground state atoms trapped in separate tweezers using the effect of Rydberg blockade. The quality of the entanglement is measured using global rotations of the internal states of both atoms.
INTRODUCTION
Entanglement, initially introduced as a quantum mechanical paradox by Einstein, Podolski and Rosen many decades ago [1], has recently been recognized as a resource for quantum information processing, for quantum metrology [2], and for the study of quantum correlated systems [3]. Entanglement is a general property of a quantum state and can be physically realized with any quantum system provided the interaction between the parts of the system can be sufficiently controlled. It has already been demonstrated in many physical systems, which include photons [4], ions [5], hybrid systems composed of an atom and a photon [6], atomic ensembles [7, 8], and superconducting circuits [9]. So far, entanglement between neutral atoms was realized using two different approaches. The first one is based on the interaction of transient atoms in a Rydberg state with a high-finesse cavity, which mediates the interaction between the atoms. Using this approach, entanglement of the atoms in different Rydberg states was demonstrated [10]. The other approach utilizes s-wave scattering between neutral atoms in optical lattices [11, 12]. Here we demonstrate the third approach based on Rydberg blockade mechanism. It allows to create entanglement between two isolated ground state neutral atoms by shortly exciting them to a Rydberg state, where they can strongly interact. This approach has been proposed in the context of quantum information processing and is in principle deterministic and scalable to larger number of atoms [13— 17].
The main aim of this proceedings paper is to give an overview of our progress in single atom manipulation and provide a qualitative understanding of the experimental methods and of the key physical effects we are using in our experiment.
SINGLE ATOM TRAPPING IN OPTICAL TWEEZERS
In our experiment, we use rubidium 87 atoms. A dipole trap, which acts as optical tweezers, is formed by a tightly focusing a laser beam to a diffraction limit of a high numerical aperture lens. The light field at the focal point of the trap is well approximated by a Gaussian beam with the waist 0.9 ^m. The wavelength of the tweezers beam is 810 nm and is detuned by 15 nm from the D1 transition of Rubidium at 795 nm. This results in a dipole trap of 1 mK depth for 0.8 mW of a laser power.
The tweezers beam is focused inside a cold cloud of atoms, formed by optical molasses, see Fig. 1a. During the simultaneous operation of the optical molasses and the tweezers, the laser light of the optical molasses plays a double role. First, atoms that enter the optical tweezers randomly are laser cooled by the molasses beams. The fluorescence light at 780 nm, which atoms emit during the laser cooling process, is collected by the same high numerical aperture objective onto an avalanche photo diode (APD) working in a single photon counting mode, see Fig. 1b. We observe in the signal distinct steps in the fluorescence rate. The lower level corresponds to the background scattered light and noise on the APD. The higher level corresponds to the fluorescence rate of a single atom inside the optical molasses. Several points on the Fig. 1b that lay between these levels correspond to the events where an atom was loaded or lost during the integration time. We do not observe events with more than one atom in the tweezers. Due to the small volume of the optical tweezers, two atoms entering simultaneously the trap illuminated by the cooling light of the optical molasses experience an inelastic light induced collision [18—19]. The released energy during these collisions, which is
Time, s
Fig. 1. (a) Optical setup for trapping single atoms. A specially designed high numerical aperture lens focuses the tweezers light (not shown) at 810 nm into an optical molasses. By sending several beams through the lens, more optical tweezers are created. The same lens is used to collect the fluorescence light at 780 nm emitted by atoms in the corresponding tweezers. (b) Typical fluorescence signal collected on an avalanche photodiode from one of the tweezers. The higher level of the fluorescence steps indicates that a single atom is trapped in the optical tweezer.
orders of magnitude higher than the tweezers depth, is converted into kinetic energy of atoms. As the result, we do not trap more than one atom inside our optical tweezers [20].
SINGLE ATOM INTERNAL STATE MANIPULATION
After detection of the high fluorescence level, the optical molasses light is switched off. All the atoms outside the optical tweezers drift away, which results in trapping of a single isolated atom.
Ground states
We consider two hyperfine levels | ^ = \F = 2, M = 2)
and = |F = 1, M = 1) of the 5s1/2 state, which are separated by 6.8 GHz, see Fig. 2a. Application of 9 G magnetic field lifts the degeneracy between the Zee-man substates effectively resulting in a clean two-level system.
We drive transition between these states using a pair of laser beams in Raman configuration. Both beams have a wavelength of795 nm and are phase locked with the frequency difference 6.8 GHz. The laser light is blue detuned by 600 MHz relative to the excited state
5P1/2 | F' = 2, M = 2). The beams are focused to 130 ^m. The laser power of 40 ^W results in a single beam Rabi frequency of17 MHz and the two photon frequency of Q= 2n x 250 kHz. The two Raman beams are in the co-propagating configuration, which insures that we drive transitions without changing the vibrational quantum number of the atom in the tweezers potential.
The internal state analysis is performed by selectively removing atoms from the tweezers. We first apply a push-out laser beam that is tuned to the transition from (5,% 2, F = 2) to (5 p3/2, F' = 3). This beam resonantly heats up and expels an atom in the state | T) out of the trap. Whereas an atom in the state | ^ remains trapped. Finally, we switch on the molasses beams and detect the presence of the atom in the tweezers by counting the fluorescence rate from the tweezers. Note that this state detection method does not discriminate between Zeeman sublevels of the F = 1 and F = 2 manifold of the 5s1/2.
To perform internal state rotation of a single atom, the following experimental sequence is applied. We first optically pump the atom into the state | T) by applying a 600 ^s long laser pulse, which is a+-polarized and tuned on the transition (5,1/2, F = 2) to (5P3/2,
Fig. 2. Rabi oscillations between the qubit states of a single atom. (a) Relevant atomic levels of a Rb atom. Two hyperfine levels are coupled by a Raman transition. (b) Measured probability to find an atom in the lower state as the function of the pulse length. Each point is an average of about 100 repetitions of the experiment.
F' = 2), together with the repumping beam tuned on the (5s1/2, F = 1) to (5 p3/2, F' = 2) transition. We then apply the pair of Raman beams for a given duration and finally detect the internal atomic state. We repeat this sequence 100 times and measure the probability to
find the atom in the state | ^. When varying the duration of the Raman pulse, we observe coherent Rabi oscillations between the states | ^ and | T), as presented in Fig. 2b. Using the model developed in the reference [21] we extract from the contrast of the oscillations an efficiency above 99% of the combined sequence of preparation, rotation and detection.
dipole trap laser light during the Rydberg excitation. During this time window, the 795 nm-laser is switched on for variable time to coherently excite the free atom to the Rydberg state. After this excitation the dipole trap is switched on again, which results in the recapture of the atom if it was in the ground state and in the loss of the atom otherwise, since atoms in the Rydberg states are not dipole trapped. We change the pulse duration by changing the duration of the infrared laser light. For every point, we repeat the experiment 100 times. Dots in the Fig 4. present the resulting Rabi oscillation between the ground and Rydberg states of one atom [22].
Rydberg states
In our experiment, one of the key ingredients of the two atom entanglement creation is the excitation of a single atom to a Rydberg state. We coherently excite an atom from the state | ^ to the state | r) = |58d3/2, F = 3, M = 3). We apply the magnetic field of 9 G to lift the degeneracy between the magnetic sublevels and to define a clean two level system | ^ to | r).
We drive the transitions between these levels using a pair of laser beams in Raman configuration, see Fig. 3. The infrared laser at 795 nm is n-polarized and is blue detuned with respect to the state 5py21F' = 2, M = 2).
The blue laser at 475 nm is a+-polarized and is stabilized to the infrared laser to exclude the relative frequency drifts of the laser frequencies. The 35 mW of the blue laser light focused to a spot of 20 ^m and the
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