process tomography of the protocol. Teleportation Between The measured average teleportation fidelity of 90% T 2% [90(2)%] over a set of mutually un- Distant Matter biased basis states, which is well above the 2/3 fidelity threshold that could be achieved classi- cally, unequivocally demonstrates the quantum S. Olmschenk,1* D. N. Matsukevich,1 P. Maunz,1 D. Hayes,1 L.-M. Duan,2 C. Monroe1 of the process (14, 15). Our teleportation protocol represents the implementation of a Quantum teleportation is the faithful transfer of quantum states between systems, relying on probabilistic measurement-based gate that could the prior establishment of entanglement and using only classical communication during the be used to generate entangled states for scalable transmission. We report teleportation of between atomic quantum memories quantum computation (16, 17). + separated by about 1 meter. A quantum stored in a single trapped ytterbium ion (Yb )is A schematic of the experimental setup (Fig. 1) + teleported to a second Yb atom with an average fidelity of 90% over a replete set of states. shows a single Yb+ atom confined and Doppler The teleportation protocol is based on the heralded entanglement of the atoms through –cooled in each of two nearly identical radio- interference and detection of emitted from each atom and guided through optical fibers. frequency (rf) Paul traps, located in independent This scheme may be used for scalable quantum computation and quantum communication. vacuum chambers (18–21). An ion will typically remain in the trap for several weeks. The defining feature of quantum physics is portation. However, a is re- states in each atom are chosen to be the first- the inherent uncertainty of physical prop- quired at both transmitting and receiving sites order magnetic field–insensitive hyperfine “clock” 2S F m 〉 Aerties, despite the fact that we observe in order to scale this protocol to quantum net- states of the 1/2 level, j ¼ 0, F ¼ 0 and only definite states after a measurement. The works and propagate quantum information over jF ¼ 1, mF ¼ 0〉, which are separated by 12.6 conventional interpretation is that the measure- multiple nodes (10). Deterministic teleportation GHz and defined to be j0〉 and j1〉, respectively. ment process itself can irreversibly influence the between quantum memories has been demon- In this notation, F is the total angular momen- quantum system under study. The field of quan- strated with trapped atomic ions in close proximity tum of the atom, and mF is its projection along a tum information science makes use of this notion to one another, relying on the mutual Coulomb quantization axis defined by an external mag- and frames quantum in terms of the interaction (11–13). In contrast to the optical sys- netic field B. The qubit exhibits times storage, processing, and communication of in- tems, these implementations feature long-lived observed to be greater than 2.5 s and thus serves formation. In particular, the back-action of mea- coherences stored in good quantum memories as an excellent quantum memory (20). surement underlies the quantum “no cloning” but lack the ability to easily transmit quantum For the teleportation protocol (Fig. 2A), the theorem, which states that it is impossible to information over long distances. states of the atomic qubits are initialized with a generate identical copies of an unknown quan- We present the implementation of a heralded 1-ms pulse of 369.5-nm light resonant with the 1 2S F 〉↔2P F 〉 tum state ( ). Nevertheless, a can teleportation protocol where the advantages from 1=2j ¼ 1 1=2 j ¼ 1 transition that op- still be transferred from one system to another both optical systems and quantum memories are tically pumps the ions to j0〉 with probability by the process of quantum teleportation (2). A combined to teleport quantum states between greater than 99% (20). We can then prepare any quantum state initially stored in system A can be two trapped ytterbium ion (Yb+) quantum superposition of j0〉 and j1〉 by applying a teleported to system B by using the resource of (qubits) over a distance of about 1 m. We fully resonant microwave pulse with controlled phase or the quantum correla- characterized the system by performing tomog- andduration(0to16ms) directly to one of the tion between systems that do not have well- raphy on the teleported states, enabling complete trap electrodes. The quantum state to be tele- defined individual properties. Relaying the result of a destructive measurement of system A al- lows the original quantum state to be recovered at system B without ever having traversed the space between the systems. The ability to teleport quantum information is an essential ingredient for the long-distance quantum communication af- forded by quantum repeaters (3)andmaybea vital component to achieve the exponential pro- cessing speed-up promised by quantum compu- tation (4). The experimental implementation of telepor- tation has been accomplished in optical sys- tems by using down-converted photons (5, 6)and squeezed light with continuous variable entangle- ment (7). Teleportation has also been accom- plished between photons and a single atomic ensemble (8, 9). Because photons are able to carry quantum information and establish entan- glement over long distances, these experiments demonstrated the nonlocal behavior of tele- + 1 Fig. 1. The experimental setup. Two Yb ions are trapped in independent vacuum chambers. An ex- JointQuantumInstitute(JQI)andDepartmentofPhysics, B University of Maryland, College Park, MD 20742, USA. 2FOCUS ternally applied magnetic field determines a quantization axis for defining the polarization of Center and Department of Physics, University of Michigan, Ann photons emitted by each atom. Spontaneously emitted photons are collected with an objective lens, Arbor, MI 48109, USA. coupled into a single-mode fiber, and directed to interfere on a beamsplitter (BS). Polarizing beamsplitters *To whom correspondence should be addressed. E-mail: (PBSs) filter out photons resulting from s decays in the atoms. The remaining p-polarized photons are [email protected] detected by single-photon counting PMTs.

486 23 JANUARY 2009 VOL 323 SCIENCE www.sciencemag.org REPORTS ported is written to ion A by using this micro- a measured mode overlap greater than 98%. Be- light is off-resonance and almost no photons are wave pulse, which prepares ion A in the state cause of the quantum interference of the two pho- scattered. By detecting the fluorescence of the jY(t1)〉A ¼ aj0〉A þ bj1〉A. A separate micro- tons, a simultaneous detection at both output atom with a single- counting photomul- wave pulse prepares ion B in the definite state ports of the beamsplitter occurs only if the pho- tiplier tube (PMT), we discriminate between j0〉 − jY(t1)〉B ¼j0〉B þj1〉B, where for simplicity tons are in the state jY 〉photons ¼jnblue 〉Ajnred 〉B − and j1〉 withanerrorofabout2%(20). we neglect normalization factors and assume jnred 〉Ajnblue 〉B (24–26), which projects the ions Measuring ion A projects ion B into one of ideal state evolution throughout our discussion. into the entangled state (27): the two states:

After this state preparation, each ion is excited − 2P 〈Y (t )j (jY(t )〉A⊗jY(t )〉B) ¼ to the 1/2 level with near-unit probability by 3 photons 3 3 Y t 〉 a 〉 b 〉 〉 an ultrafast laser pulse (≈1 ps) having a linear j ( 5) B ¼ j1 B þ j0 B (if measured j0 A) jY(t )〉 ¼ aj0〉Aj1〉B − bj1〉Aj0〉B (2) polarization aligned parallel to the quantization 3 ions Y(t )〉B a 1〉B − b 0〉B (if measured 1〉A) axis (p-polarized) and a central wavelength of A coincident detection of two photons is there- j 5 ¼ j j j 369.5 nm. Due to the polarization of the pulse and fore the heralding event that announces the suc- (4) atomic selection rules, the broadband pulse coher- cess of the ion-ion entangling gate operation 〉 2P F m 〉 1s% A s% As% B − s% As% B s% i A ently transfers j0 to 1=2j ¼ 1, F ¼ 0 and 2 3 ( 0 0 3 3 ), where 0 is the identity and The result of the measurement on ion is 〉 2P F m 〉 22 s% i z i j1 to 1=2j ¼ 0, F ¼ 0 (Fig. 2B) ( ). Be- 3 the -Pauli operator acting on the th qubit relayed through a classical communication chan- cause the duration of this pulse is much shorter (16). In the current setup, this entangling gate only nel and used to determine the necessary phase t ≈ 2P P ≈ : −8 p than the 8 ns natural lifetime of the 1=2 succeeds with probability gate 2 2 10 ,lim- of a conditional microwave pulse applied to level, each ion spontaneously emits a single pho- ited by the efficiency of collecting and detecting ion B to recover the state initially written to ion 2S 18 A 〉 R p ton while returning to the 1=2 ( ). both spontaneously emitted photons. Therefore, ; measuring j0 A requires the rotation x( ), The emitted photons at 369.5 nm can each be the previous steps (state preparation and pulsed whereas j1〉A demands Ry(p). Afterward, the state collected along a direction perpendicular to the excitation) are repeated at a rate of 40 to 75 kHz, of ion B is ideally jY(t6)〉B ¼ aj0〉B þ bj1〉B, quantization axis by objective lenses of numerical including intermittent cooling, until the gate opera- which completes the teleportation of the quan- aperture NA = 0.23 and coupled into single-mode tion is successful (every 12 min, on average). Be- tum state between the two distant matter qubits. fibers. Observation along this direction allows for cause each attempt is independent of all others, this The teleportation protocol we present differs polarization filtering of the emitted photons because protocol allows for a sequence of unknown and from the original proposal (2)inthatweuse those produced by p and s transitions appear as unrelated input states. After the entanglement has four qubits (two atoms and two photons) rather orthogonally polarized (23). Considering only p been confirmed by the heralding event, another than three, and our implementation is intrinsical- decays results in each ion being entangled with pulse of microwaves transforms the state of ion ly probabilistic because the two-photon Bell the frequency of its emitted photon such that A through the rotation operator Ryðp=2Þ, altering states are not all deterministically distinguish- the state of the ions given in Eq. 2 to able (5, 26, 27). Nevertheless, the heralding event of the two-photon coincident detection still al- Y t 〉 a 〉 n 〉 b 〉 n 〉 j ( 2) A ¼ j0 Aj blue A þ j1 Aj red A jY(t4)〉ions ¼ a(j0〉A þj1〉A)j1〉B − lows our teleportation protocol to succeed with- out postselection (15). In addition, establishing jY(t2)〉B ¼j0〉Bjnblue〉B þj1〉Bjnred〉B (1) b(−j0〉A þj1〉A)j0〉B (3) the between the (atomic) quan- where jnblue 〉 and jnred〉 are single photon states We then measure the state of ion A with stan- tum memories with photons and entanglement having well-resolved frequencies nblue and nred, dard fluorescence techniques, by illuminating swapping allows the atoms to be separated by a each with a bandwidth of 1/(2pt) ≈ 20 MHz the ion with laser light at 369.5 nm, resonant large distance from the outset. 2 2 and frequency difference vblue – vred = 14.7 GHz. with the S1=2 jF ¼ 1〉↔ P1=2jF ¼ 0〉 transition. A successful implementation of this telepor- The outputs of the fibers are directed to inter- If the ion is in the state j1〉, it scatters many tation protocol requires the transmission of two fere at a 50:50 nonpolarizing beamsplitter, with photons, whereas if the ion is in the state j0〉 the classical bits of information: one to announce


Fig. 2. (A) Schematic of the teleportation protocol. Each ion is first initialized ion entangling gate (t3). If the gate is successful, ion A is rotated by p/2 (t4)and to j0〉 by optical pumping. The state to be teleported is written to ion A by a measured (t5). A microwave pulse with phase conditioned on the outcome of microwave pulse, whereas a separate microwave pulse prepares ion B in a the measurement on ion A is then applied to ion B to complete the known superposition (t1). A laser pulse excites each atom, as shown in (B). The teleportation of the quantum state (t6). (B) Ion-photon entanglement process. A frequency of an emitted p-polarized photon (selected by polarization filtering) broadband picosecond pulse with a central wavelength at 369.5 nm is used to 2 is then entangled with the hyperfine levels of the atom (t2). These two photons coherently excite j0〉 and j1〉 to the P1/2 level. Because of the atomic selection interfere at a BS, as illustrated in Fig. 1, resulting in a coincident detection only rules and polarization filtering with PBSs to only observe photons from a p − ifthephotonsareinthejY 〉photons state, which heralds the success of the ion- decay, the coherence of the atomic states is retained.

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Fig. 3. Tomography of the teleported quantum states. The reconstructed density jYideal〉 = j0〉 teleported with fidelity f = 0.93(4), and (F) jYideal 〉 = j1〉 matrices, r, for the six unbiased basis states teleported from ion A to ion B:(A) teleported with fidelity f = 0.88(4). These measurements yield an average tele- jYideal〉 = j0〉 + j1〉 teleported with fidelity f =0.91(3),(B) jYideal〉 = j0〉 – j1〉 portation fidelity f = 0:90(2), where we have defined the fidelity as the overlap of teleported with fidelity f = 0.88(4), (C) jYideal〉 = j0〉 + ij1〉 teleported with fidelity the ideal teleported state with the measured , f = 〈Yideal jrjYideal 〉. f =0.92(4),(D) jYideal〉 = j0〉 – ij1〉 teleported with fidelity f = 0.91(4), (E) The data shown comprise a total of 1285 events in 253 hours.

the success of the entangling gate and another to Fig. 4. Absolute value of the compo- determine the proper final rotation to recover the nents of the reconstructed process matrix, teleported state at ion B. Although these clas- jclkj,withl, k =0,1,2,and3.Thestate sical bits do not contain any information about a tomography of the six mutually unbiased or b, in the absence of this classical information basis states teleported between the two ion B is left in a mixed state (Eq. 4), and the ions, displayed in Fig. 3, enables process protocol fails. The required classical communi- tomography of the teleportation protocol by a maximum likelihood method. The cation assures that no information is transferred s% i superluminally (2). operators i are the identity ( =0)and the x-, y-, and z- (i =1,2, We evaluate the teleportation protocol by per- and 3). As intended, the dominant com- forming state tomography on each teleported ponent of c is the contribution of the state. The tomographic reconstruction of the identity operation, yielding an overall single-qubit density matrix can be completed by process fidelity fprocess = tr(cideal c)= measuring the state in three mutually unbiased 0.84(2), consistent with the average fi- measurement bases. Because measurement of the delity cited above. ion occurs via the aforementioned state fluores- cence technique, measurement in the remain- ing two bases requires an additional microwave pulse before detection; we define the rotation {Ry(p/2), Rx(p/2), R(0)} before detection to cor- respond to measurement in the basis {x, y, z}. The single-qubit density matrix is then recon- The reconstructed density matrices also fa- this is consistent with the average fidelity found structed from these measurements with use of a cilitate full characterization of the teleportation above (30). simple analytical expression (28). protocol by quantum process tomography. We The deviation from unit average fidelity is con- We teleport and perform tomography on the can completely describe the effect of the tele- sistent with known experimental errors. The pri- Y 〉 ∈ r set of six mutually unbiased basis states j ideal portation protocol on an input state in by de- mary sources that reduce the average fidelity are fj0〉 þj1〉,j0〉 −j1〉,j0〉 þ ij1〉,j0〉 − ij1〉,j0〉,j1〉g. termining the process matrix c, defined by r ¼ imperfect state detection (3.5%), photon mode mis- r The reconstructed density matrix, , for each of 3 matchatthe50:50beamsplitter(4%),andpolar- these teleported states is shown in Fig. 3. The ∑ clks% lrins% k , where to evaluate our process ization mixing resulting from the nonzero numerical fidelity of the teleportation, defined as the over- l, k¼0 aperture of the objective lens and from misalign- r Y 〉〈Y lap of the ideal teleported state and the measured we take in ¼j ideal idealj. The ideal process ment with respect to the magnetic field (2%). Other density matrix f ¼ 〈YidealjrjYideal〉,forthisset matrix, cideal, has only one nonzero component, sources, including incomplete state preparation, f c of states is measured to be = {0.91(3), 0.88(4), ð idealÞ00 ¼ 1, meaning the input state is faith- pulsed excitation to the wrong atomic state, dark 0.92(4), 0.91(4), 0.93(4), 0.88(4)}, yielding an fully teleported. We experimentally determine the counts of the PMT leading to false coincidence average teleportation fidelity f ¼ 0:90ð2Þ.The process matrix c (Fig. 4) by using a maximum events, photon polarization rotation while travers- experimental teleportation fidelities surpass the likelihood method (29) and calculate the process ing the , and multiple excitation result- maximum value of 2/3 that is achievable by clas- fidelitytobefprocess = tr(cideal c) = 0.84(2). ing from pulsed laser light leakage, are each expected sical means, explicitly demonstrating the quan- Given that the relation between the average fi- to contribute to the error by much less than 1%. tum nature of the process (14, 15). delity and process fidelity is fprocess ¼ (3 f − 1)/2, Residual micromotion at the rf-drive frequency of

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Fe-N bond elongation by ~0.2 Å in the HS com- Femtosecond XANES Study of the pared to the LS state (1, 2). Theoretical studies show that the Fe-N bond length of the singlet and Light-Induced Crossover triplet metal-centered (MC) 1,3T states lies half- way between those of the LS and HS states (7). Obviously, accessing the HS by Dynamics in an Iron(II) Complex absorption of light from the LS ground state is forbidden by the spin selection rules. Therefore, Ch. Bressler,1 C. Milne,1 V.-T. Pham,1 A. ElNahhas,1 R. M. van der Veen,1,2 1,2 2 2 2 1,2 the doorway to the HS state is ideally via the W. Gawelda, * S. Johnson, P. Beaud, D. Grolimund, M. Kaiser, singlet metal-to-ligand-charge-transfer (1MLCT) 2 2 2 1† C. N. Borca, G. Ingold, R. Abela, M. Chergui that exhibits strong absorption bands in the visi- ble spectrum, or via the weakly absorbing and X-ray absorption spectroscopy is a powerful probe of molecular structure, but it has previously been lower-lying 1,3T states (1, 2).Thetimescaleand too slow to track the earliest dynamics after photoexcitation. We investigated the ultrafast the route going from the initially excited 1MLCT formation of the lowest quintet state of aqueous iron(II) tris(bipyridine) upon excitation of the 1 state to the lowest-lying quintet state are still the singlet metal-to-ligand-charge-transfer ( MLCT) state by femtosecond optical pump/x-ray probe subject of debate. Steady-state spectroscopic studies techniques based on x-ray absorption near-edge structure (XANES). By recording the intensity at cryogenic temperatures showed that excitation of a characteristic XANES feature as a function of laser pump/x-ray probe time delay, we find that into the MC 1,3T states leads to population of the the quintet state is populated in about 150 femtoseconds. The quintet state is further evidenced by 5 T2 state with a quantum efficiency of ~80% (2). its full XANES spectrum recorded at a 300-femtosecond time delay. These results resolve a Researchers therefore concluded that the relaxa- long-standing issue about the population mechanism of quintet states in iron(II)-based tion cascade from the 1MLCT state to the HS 5T 1 →3 →5 2 complexes, which we identify as a simple MLCT MLCT T cascade from the initially state proceeds via the intermediate 1,3Tstates. 3 →5 excited state. The time scale of the MLCT T relaxation corresponds to the period of the However, for excitation of the 1MLCT state, the iron-nitrogen stretch vibration. relaxation process was reported to occur with 100% efficiency at both 10 K (2) and at room here is a large class of iron(II)-based The SCO phenomenon has been much studied 2 3–6 molecular complexes that exhibit two using steady-state ( ) and ultrafast ( ) optical 1EcolePolytechniqueFédéraledeLausanne,Laboratoirede electronic states closely spaced in energy: spectroscopies, with the goal of identifying the Spectroscopie Ultrarapide, ISIC, FSB-BSP, CH-1015 Lausanne, T 2 a low-spin (LS) singlet and a high-spin (HS) elementary steps leading to formation of the HS Switzerland. Swiss Light Source, Paul-Scherrer Institut, CH-5232 quintet state. They therefore manifest spin cross- state. A representative diagram of all Villigen PSI, Switzerland. over (SCO) behavior, wherein conversion from a Fe(II)-based complexes is shown in Fig. 1 (7). *Present address: Laser Processing Group, Instituto de Optica, Consejo Superior de Investigaciones Científicas, Serrano 121, LS ground state to a HS excited state (or the The main difference between them concerns the E-28006 Madrid, Spain. reverse) can be induced by small temperature or absolute energies of states, not their energetic or- †To whom correspondence should be addressed. E-mail: pressure changes or by light absorption (1, 2). dering (2). All crystallographic studies point to an [email protected]

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