Fusion of deterministically generated photonic graph states.

Entanglement has evolved from an enigmatic concept of quantum physics to a key ingredient of quantum technology. It explains correlations between measurement outcomes that contradict classical physics and has been widely explored with small sets of individual qubits. Multi-partite entangled states build up in gate-based quantum-computing protocols and-from a broader perspective-were proposed as the main resource for measurement-based quantum-information processing1,2. The latter requires the ex-ante generation of a multi-qubit entangled state described by a graph3-6. Small graph states such as Bell or linear cluster states have been produced with photons7-16, but the proposed quantum-computing and quantum-networking applications require fusion of such states into larger and more powerful states in a programmable fashion17-21. Here we achieve this goal by using an optical resonator22 containing two individually addressable atoms23,24. Ring25 and tree26 graph states with up to eight qubits, with the names reflecting the entanglement topology, are efficiently fused from the photonic states emitted by the individual atoms. The fusion process itself uses a cavity-assisted gate between the two atoms. Our technique is, in principle, scalable to even larger numbers of qubits and is the decisive step towards, for instance, a memory-less quantum repeater in a future quantum internet27-29.

Efficient generation of entangled multiphoton graph states from a single atom.

The central technological appeal of quantum science resides in exploiting quantum effects, such as entanglement, for a variety of applications, including computing, communication and sensing1. The overarching challenge in these fields is to address, control and protect systems of many qubits against decoherence2. Against this backdrop, optical photons, naturally robust and easy to manipulate, represent ideal qubit carriers. However, the most successful technique so far for creating photonic entanglement3 is inherently probabilistic and, therefore, subject to severe scalability limitations. Here we report the implementation of a deterministic protocol4-6 for the creation of photonic entanglement with a single memory atom in a cavity7. We interleave controlled single-photon emissions with tailored atomic qubit rotations to efficiently grow Greenberger-Horne-Zeilinger (GHZ) states8 of up to 14 photons and linear cluster states9 of up to 12 photons with a fidelity lower bounded by 76(6)% and 56(4)%, respectively. Thanks to a source-to-detection efficiency of 43.18(7)% per photon, we measure these large states about once every minute, which is orders of magnitude faster than in any previous experiment3,10-13. In the future, this rate could be increased even further, the scheme could be extended to two atoms in a cavity14,15 or several sources could be quantum mechanically coupled16, to generate higher-dimensional cluster states17. Overcoming the limitations encountered by probabilistic schemes for photonic entanglement generation, our results may offer a way towards scalable measurement-based quantum computation18,19 and communication20,21.

Nondestructive detection of photonic qubits.

One of the biggest challenges in experimental quantum information is to sustain the fragile superposition state of a qubit1. Long lifetimes can be achieved for material qubit carriers as memories2, at least in principle, but not for propagating photons that are rapidly lost by absorption, diffraction or scattering3. The loss problem can be mitigated with a nondestructive photonic qubit detector that heralds the photon without destroying the encoded qubit. Such a detector is envisioned to facilitate protocols in which distributed tasks depend on the successful dissemination of photonic qubits4,5, improve loss-sensitive qubit measurements6,7 and enable certain quantum key distribution attacks8. Here we demonstrate such a detector based on a single atom in two crossed fibre-based optical resonators, one for qubit-insensitive atom-photon coupling and the other for atomic-state detection9. We achieve a nondestructive detection efficiency upon qubit survival of 79 ± 3 per cent and a photon survival probability of 31 ± 1 per cent, and we preserve the qubit information with a fidelity of 96.2 ± 0.3 per cent. To illustrate the potential of our detector, we show that it can, with the current parameters, improve the rate and fidelity of long-distance entanglement and quantum state distribution compared to previous methods, provide resource optimization via qubit amplification and enable detection-loophole-free Bell tests.

A photon-photon quantum gate based on a single atom in an optical resonator.

That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing. The long-standing challenge here is to realize a deterministic photon-photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other's phase by π radians. For polarization qubits, this amounts to the conditional flipping of one photon's polarization to an orthogonal state. So far, only probabilistic gates based on linear optics and photon detectors have been realized, because "no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift''. Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments. Platforms range from Rydberg blockade in atomic ensembles to single-atom cavity quantum electrodynamics. Applications such as single-photon switches and transistors, two-photon gateways, nondestructive photon detectors, photon routers and nonlinear phase shifters have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light-matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan-Kimble protocol of a universal controlled phase flip (π phase shift) photon-photon quantum gate. We achieve an average gate fidelity of (76.2 ± 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon-photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations. The demonstrated feasibility of deterministic protocols for the optical processing of quantum information could lead to new applications in which photons are essential, especially long-distance quantum communication and scalable quantum computing.

High-Resolution "Magic"-Field Spectroscopy on Trapped Polyatomic Molecules.

Rapid progress in cooling and trapping of molecules has enabled first experiments on high-resolution spectroscopy of trapped diatomic molecules, promising unprecedented precision. Extending this work to polyatomic molecules provides unique opportunities due to more complex geometries and additional internal degrees of freedom. Here, this is achieved by combining a homogeneous-field microstructured electric trap, rotational transitions with minimal Stark broadening at a"magic" offset electric field, and optoelectrical Sisyphus cooling of molecules to the low millikelvin temperature regime. We thereby reduce Stark broadening on the J=5←4 (K=3) transition of formaldehyde at 364 GHz to well below 1 kHz, observe Doppler-limited linewidths down to 3.8 kHz, and determine the magic-field line position with an uncertainty below 100 Hz. Our approach opens a multitude of possibilities for investigating diverse polyatomic molecule species.

Quantum Teleportation between Remote Qubit Memories with Only a Single Photon as a Resource.

Quantum teleportation enables the deterministic exchange of qubits via lossy channels. While it is commonly believed that unconditional teleportation requires a preshared entangled qubit pair, here we demonstrate a protocol that is in principle unconditional and requires only a single photon as an ex-ante prepared resource. The photon successively interacts, first, with the receiver and then with the sender qubit memory. Its detection, followed by classical communication, heralds a successful teleportation. We teleport six mutually unbiased qubit states with average fidelity F[over ¯]=(88.3±1.3)% at a rate of 6 Hz over 60 m.

Detecting an Itinerant Optical Photon Twice without Destroying It.

Nondestructive quantum measurements are central for quantum physics applications ranging from quantum sensing to quantum computing and quantum communication. Employing the toolbox of cavity quantum electrodynamics, we here concatenate two identical nondestructive photon detectors to repeatedly detect and track a single photon propagating through a 60 m long optical fiber. By demonstrating that the combined signal-to-noise ratio of the two detectors surpasses each single one by about 2 orders of magnitude, we experimentally verify a key practical benefit of cascaded nondemolition detectors compared to conventional absorbing devices.

Continuous Generation of Quantum Light from a Single Ground-State Atom in an Optical Cavity.

We show an optical wave-mixing scheme that generates quantum light by means of a single three-level atom. The atom couples to an optical cavity and two laser fields that together drive a cycling current within the atom. Weak driving in combination with strong atom-cavity coupling induces transitions in a harmonic ladder of dark states, accompanied by single-photon emission via a quantum Zeno effect and suppression of atomic excitation via quantum interference. For strong driving, the system can generate coherent or Schrödinger cat-like fields with frequencies distinct from those of the applied lasers.

A quantum gate between a flying optical photon and a single trapped atom.

The steady increase in control over individual quantum systems supports the promotion of a quantum technology that could provide functionalities beyond those of any classical device. Two particularly promising applications have been explored during the past decade: photon-based quantum communication, which guarantees unbreakable encryption but which still has to be scaled to high rates over large distances, and quantum computation, which will fundamentally enhance computability if it can be scaled to a large number of quantum bits (qubits). It was realized early on that a hybrid system of light qubits and matter qubits could solve the scalability problem of each field--that of communication by use of quantum repeaters, and that of computation by use of an optical interconnect between smaller quantum processors. To this end, the development of a robust two-qubit gate that allows the linking of distant computational nodes is "a pressing challenge". Here we demonstrate such a quantum gate between the spin state of a single trapped atom and the polarization state of an optical photon contained in a faint laser pulse. The gate mechanism presented is deterministic and robust, and is expected to be applicable to almost any matter qubit. It is based on reflection of the photonic qubit from a cavity that provides strong light-matter coupling. To demonstrate its versatility, we use the quantum gate to create atom-photon, atom-photon-photon and photon-photon entangled states from separable input states. We expect our experiment to enable various applications, including the generation of atomic and photonic cluster states and Schrödinger-cat states, deterministic photonic Bell-state measurements, scalable quantum computation and quantum communication using a redundant quantum parity code.

Single-Photon Distillation via a Photonic Parity Measurement Using Cavity QED.

Single photons with tailored temporal profiles are a vital resource for future quantum networks. Here we distill them out of custom-shaped laser pulses that reflect from a single atom strongly coupled to an optical resonator. A subsequent measurement on the atom is employed to herald a successful distillation. Out of vacuum-dominated light pulses, we create single photons with fidelity 66(1)%, two-and-more-photon suppression 95.5(6)%, and a Wigner function with negative value -0.125(6). Our scheme applied to state-of-the-art fiber resonators could boost the single-photon fidelity to up to 96%.

An elementary quantum network of single atoms in optical cavities.

Quantum networks are distributed quantum many-body systems with tailored topology and controlled information exchange. They are the backbone of distributed quantum computing architectures and quantum communication. Here we present a prototype of such a quantum network based on single atoms embedded in optical cavities. We show that atom-cavity systems form universal nodes capable of sending, receiving, storing and releasing photonic quantum information. Quantum connectivity between nodes is achieved in the conceptually most fundamental way-by the coherent exchange of a single photon. We demonstrate the faithful transfer of an atomic quantum state and the creation of entanglement between two identical nodes in separate laboratories. The non-local state that is created is manipulated by local quantum bit (qubit) rotation. This efficient cavity-based approach to quantum networking is particularly promising because it offers a clear perspective for scalability, thus paving the way towards large-scale quantum networks and their applications.

Sisyphus cooling of electrically trapped polyatomic molecules.

Polar molecules have a rich internal structure and long-range dipole-dipole interactions, making them useful for quantum-controlled applications and fundamental investigations. Their potential fully unfolds at ultracold temperatures, where various effects are predicted in many-body physics, quantum information science, ultracold chemistry and physics beyond the standard model. Whereas a wide range of methods to produce cold molecular ensembles have been developed, the cooling of polyatomic molecules (that is, with three or more atoms) to ultracold temperatures has seemed intractable. Here we report the experimental realization of optoelectrical cooling, a recently proposed cooling and accumulation method for polar molecules. Its key attribute is the removal of a large fraction of a molecule's kinetic energy in each cycle of the cooling sequence via a Sisyphus effect, allowing cooling with only a few repetitions of the dissipative decay process. We demonstrate the potential of optoelectrical cooling by reducing the temperature of about one million CH(3)F molecules by a factor of 13.5, with the phase-space density increased by a factor of 29 (or a factor of 70 discounting trap losses). In contrast to other cooling mechanisms, our scheme proceeds in a trap, cools in all three dimensions and should work for a large variety of polar molecules. With no fundamental temperature limit anticipated down to the photon-recoil temperature in the nanokelvin range, we expect our method to be able to produce ultracold polyatomic molecules. The low temperatures, large molecule numbers and long trapping times of up to 27 seconds should allow an interaction-dominated regime to be attained, enabling collision studies and investigation of evaporative cooling towards a Bose-Einstein condensate of polyatomic molecules.

Cavity Carving of Atomic Bell States.

We demonstrate entanglement generation of two neutral atoms trapped inside an optical cavity. Entanglement is created from initially separable two-atom states through carving with weak photon pulses reflected from the cavity. A polarization rotation of the photons heralds the entanglement. We show the successful implementation of two different protocols and the generation of all four Bell states with a maximum fidelity of (90±2)%. The protocol works for any distance between cavity-coupled atoms, and no individual addressing is required. Our result constitutes an important step towards applications in quantum networks, e.g., for entanglement swapping in a quantum repeater.

Two-Photon Blockade in an Atom-Driven Cavity QED System.

Photon blockade is a dynamical quantum-nonlinear effect in driven systems with an anharmonic energy ladder. For a single atom strongly coupled to an optical cavity, we show that atom driving gives a decisively larger optical nonlinearity than cavity driving. This enhances single-photon blockade and allows for the implementation of two-photon blockade where the absorption of two photons suppresses the absorption of further photons. As a signature, we report on three-photon antibunching with simultaneous two-photon bunching observed in the light emitted from the cavity. Our experiment constitutes a significant step towards multiphoton quantum-nonlinear optics.

A single-atom quantum memory.

The faithful storage of a quantum bit (qubit) of light is essential for long-distance quantum communication, quantum networking and distributed quantum computing. The required optical quantum memory must be able to receive and recreate the photonic qubit; additionally, it must store an unknown quantum state of light better than any classical device. So far, these two requirements have been met only by ensembles of material particles that store the information in collective excitations. Recent developments, however, have paved the way for an approach in which the information exchange occurs between single quanta of light and matter. This single-particle approach allows the material qubit to be addressed, which has fundamental advantages for realistic implementations. First, it enables a heralding mechanism that signals the successful storage of a photon by means of state detection; this can be used to combat inevitable losses and finite efficiencies. Second, it allows for individual qubit manipulations, opening up avenues for in situ processing of the stored quantum information. Here we demonstrate the most fundamental implementation of such a quantum memory, by mapping arbitrary polarization states of light into and out of a single atom trapped inside an optical cavity. The memory performance is tested with weak coherent pulses and analysed using full quantum process tomography. The average fidelity is measured to be 93%, and low decoherence rates result in qubit coherence times exceeding 180 microseconds. This makes our system a versatile quantum node with excellent prospects for applications in optical quantum gates and quantum repeaters.

Optoelectrical Cooling of Polar Molecules to Submillikelvin Temperatures.

We demonstrate direct cooling of gaseous formaldehyde (H2CO) to the microkelvin regime. Our approach, optoelectrical Sisyphus cooling, provides a simple dissipative cooling method applicable to electrically trapped dipolar molecules. By reducing the temperature by 3 orders of magnitude and increasing the phase-space density by a factor of ∼10(4), we generate an ensemble of 3×10(5) molecules with a temperature of about 420 µK, populating a single rotational state with more than 80% purity.

Thermometry of Guided Molecular Beams from a Cryogenic Buffer-Gas Cell.

A comprehensive characterisation of cold molecular beams from a cryogenic buffer-gas cell, providing insight into the physics of buffer-gas cooling, is presented. Cold molecular beams are extracted from a cryogenic cell by electrostatic guiding, which is also used to measure their velocity distribution. The rotational-state distribution of the molecules is probed by radio-frequency resonant depletion spectroscopy. With the help of complete trajectory simulations, yielding the guiding efficiency for all of the thermally populated states, it is possible to determine both the rotational and the translational temperature of the molecules at the output of the buffer-gas cell. This thermometry method is demonstrated for various regimes of buffer-gas cooling and beam formation as well as for molecular species of different sizes (CH3 F and CF3 CCH). Comparison of the rotational and translational temperatures provides evidence of faster rotational thermalisation for the CH3 F/He system in the limit of low He density. In addition, the relaxation rates for different rotational states appear to be different.

Electromagnetically induced transparency with single atoms in a cavity.

Optical nonlinearities offer unique possibilities for the control of light with light. A prominent example is electromagnetically induced transparency (EIT), where the transmission of a probe beam through an optically dense medium is manipulated by means of a control beam. Scaling such experiments into the quantum domain with one (or just a few) particles of light and matter will allow for the implementation of quantum computing protocols with atoms and photons, or the realization of strongly interacting photon gases exhibiting quantum phase transitions of light. Reaching these aims is challenging and requires an enhanced matter-light interaction, as provided by cavity quantum electrodynamics. Here we demonstrate EIT with a single atom quasi-permanently trapped inside a high-finesse optical cavity. The atom acts as a quantum-optical transistor with the ability to coherently control the transmission of light through the cavity. We investigate the scaling of EIT when the atom number is increased one-by-one. The measured spectra are in excellent agreement with a theoretical model. Merging EIT with cavity quantum electrodynamics and single quanta of matter is likely to become the cornerstone for novel applications, such as dynamic control of the photon statistics of propagating light fields or the engineering of Fock state superpositions of flying light pulses.

Heralded Storage of a Photonic Quantum Bit in a Single Atom.

Combining techniques of cavity quantum electrodynamics, quantum measurement, and quantum feedback, we have realized the heralded transfer of a polarization qubit from a photon onto a single atom with 39% efficiency and 86% fidelity. The reverse process, namely, qubit transfer from the atom onto a given photon, is demonstrated with 88% fidelity and an estimated efficiency of up to 69%. In contrast to previous work based on two-photon interference, our scheme is robust against photon arrival-time jitter and achieves much higher efficiencies. Thus, it constitutes a key step toward the implementation of a long-distance quantum network.

Rotational Cooling of Trapped Polyatomic Molecules.

Controlling the internal degrees of freedom is a key challenge for applications of cold and ultracold molecules. Here, we demonstrate rotational-state cooling of trapped methyl fluoride molecules (CH_{3}F) by optically pumping the population of 16 M sublevels in the rotational states J=3, 4, 5 and 6 into a single level. By combining rotational-state cooling with motional cooling, we increase the relative number of molecules in the state J=4, K=3, M=4 from a few percent to over 70%, thereby generating a translationally cold (≈30 mK) and nearly pure state ensemble of about 10^{6} molecules. Our scheme is extendable to larger sets of initial states, other final states, and a variety of molecule species, thus paving the way for internal-state control of ever-larger molecules.