We report on the preparation and detection of entangled states between an electron spin 1/2 and a nuclear spin 1/2 in a molecular single crystal. These were created by applying pulses at ESR (9.5 GHz) and NMR (28 MHz) frequencies. Entanglement was detected by using a special entanglement detector sequence based on a unitary back transformation including phase rotation.PACS numbers: 03.67.-a, 03.65. Ud, 33.35.+r, The entanglement between two spins 1/2 is at the heart of quantum mechanics. Ever since a so-called "paradox" was formulated by Einstein, Podolsky and Rosen (EPR) [1], referring to local measurements performed on the individual spins of a delocalized entangled pair, properties of entanglement and its consequences for quantum physics has been discussed in great detail [2]. In the context of quantum information processing (QIP) entanglement has been considered as a resource for quantum parallelism (speedup of quantum computing) [3,4,5] and quantum cryptography [6,7]. A number of these quantum algorithms have been demonstrated in NMR (nuclear magnetic resonance) quantum computing [8,9,10].In this contribution we report on the experimental preparation and observation of the entangled states of an electron spin S = 1/2 and a nuclear spin I = 1/2 in a crystalline solid. The spins considered here are a proton and a radical (unpaired electron spin) produced by x-ray irradiation of a malonic acid single crystal [11]. This leads to the partial conversion of the CH 2 group of the malonic acid molecule to the radical• CH where the dot marks the electron spin. In a strong magnetic field the following four Zeeman product states |m S m I = | ↑↑ , | ↑↓ , | ↓↑ , | ↓↓ exist where the arrows label the ±1/2 states of the electron and the nuclear spin. Equivalently we will use a qubit labelling as |m S m I = |00 , |01 , |10 , |11 . The energy level diagram corresponding to the electron-proton spin system is shown in fig. 1, where we have also indicated the possible ESR (∆m S = ±1) and NMR transitions (∆m I = ±1) of the individual spins by solid arrows.What we are aiming at are states of the typeThese represent all four possible entangled states of a two qubit system, also called the Bell states of two spins 1/2. They correspond to a superposition of the states in fig. 1 connected by dashed arrows. Electron spin resonance (ESR) was performed at Xband (9.49 GHz) at T = 40 K. The low temperature was chosen only for reasons of signal-to-noise ratio. The two well resolved ESR lines due to the • CH proton depend on the orientation of the single crystal and were observed at magnetic fields of 338.2 mT and 339.2 mT with a linewidth of 0.5 mT for the ESR and about 1 MHz for the ENDOR (electron nuclear double resonance) line. This orientation corresponds to a principal axis of the hyperfine tensor. There are two different proton NMR transitions. We applied pulsed ENDOR techniques to one of them at the frequency of 28.05 MHz.In the high temperature approximation we express the Boltzmann spin density matrix asρ B = (1 − K B ) 1 41 + K B...

We have prepared combined electron and nuclear spin pseudoentangled states 27 and 18 out of the total number of eight quantum states in the multilevel quantum system of a nitrogen atom with electron spin 3=2 and nuclear spin 1=2 encaged in the endohedral fullerene 15 N@C 60 . Density matrix tomography was applied to verify the degree of entanglement.

Procedures of the preparation and detection of entangled electron-nuclear spin states in (15)N@C(60) by combining electron spin resonance and electron nuclear double resonance pulse techniques are presented. A quantitative evaluation of the complete density matrix is obtained by a special density matrix tomography. All four Bell states of a two qubit subsystem were analyzed and experimental decoherence times are presented. In addition, we estimate a quantum critical temperature of T(q)=7.76 K for this system at an electron spin resonance frequency of 95 GHz.

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