We propose and experimentally verify a scheme to engineer arbitrary states of traveling light field up to the two-photon level. The desired state is remotely prepared in the signal channel of spontaneous parametric down-conversion by means of conditional measurements on the idler channel. The measurement consists of bringing the idler field into interference with two ancilla coherent states, followed by two single-photon detectors, which, in coincidence, herald the preparation event. By varying the amplitudes and phases of the ancillae, we can prepare any arbitrary superposition of zero-one-and two-photon states. PACS numbers:Modern quantum information science relies upon two key concepts -superposition and entanglement. As fundamental tenets of quantum mechanics, they govern the way information can be shared, transferred or measured. This information lives in a Hilbert space, in the form of a quantum state. Consequently, the ability to actively control the coherent dynamics of a quantum state is paramount for quantum information technology. This task forms the essence of quantum state engineering (QSE). In the optical domain, a widely-used approach for QSE involves generating a "primitive" quantum state and then manipulating it, for example, by bringing it into interaction with an ancillary system. Employing appropriate measurements, the ancilla is then traced out, leading to reduction of the overall system to the desired target state, ready to be detected and characterized.In modern quantum optics, the "primitive" is commonly the state of correlated photon pairs produced in spontaneous parametric down conversion (SPDC). Conditional photon detection on one or both channels is then employed to produce the state of interest. This technique has been successfully applied to engineer complex entangled states of dual-rail optical qubits [1], albeit mostly in a postselected manner: we do not know that the state has been prepared until it is detected and destroyed. A fundamental impediment to optical QSE arises because equidistant energy levels of a harmonic oscillator (such as an electromagnetic mode) cannot be individually accessed using classical control signals. Outside the optical domain, this challenge has been addressed in ion traps [8] and high-Q microwave cavities [9] by coupling the oscillator energy eigenstates to a two-level atomic or spin system [10]. Very recently, arbitrary superposition of Fock states were synthesized inside a superconducting cavity by means of coupling to a Josephson phase qubit [11]. However, the loss of coherence in this scheme provides a fundamental limitation to the obtainable accuracy and complexity of the prepared state.While traveling field implementations do not suffer from this kind of decoherence and also automatically satisfy DiVincenzo's criterion of "flying qubits" [12], they are still beset with the problem of inefficiencies and losses. There exist a number of theoretical proposals for implementing optical QSE [reviewed in detail in [13]], for example, using coherent disp...

We present a comprehensive theory and an easy to follow method for the design and construction of a wideband homodyne detector for time-domain quantum measurements. We show how one can evaluate the performance of a detector in a specific time-domain experiment based on electronic spectral characteristic of that detector. We then present and characterize a high-performance detector constructed using inexpensive, commercially available components such as low-noise high-speed operational amplifiers and high-bandwidth photodiodes. Our detector shows linear behavior up to a level of over 13 dB clearance between shot noise and electronic noise, in the range from DC to 100 MHz. The detector can be used for measuring quantum optical field quadratures both in the continuous-wave and pulsed regimes with pulse repetition rates up to about 250 MHz.

We demonstrate efficient heralded generation of high purity narrow-bandwidth single photons from a transient collective spin excitation in a hot atomic vapour cell. Employing optical homodyne tomography, we fully reconstruct the density matrix of the generated photon and observe a Wigner function reaching the zero value without correcting for any inefficiencies. The narrow bandwidth of the photon produced is accompanied by a high generation rate yielding a high spectral brightness. The source is therefore compatible with atomic-based quantum memories as well as other applications in light-atom interfacing. This work paves the way to preparing and measuring arbitrary superposition states of collective atomic excitations. [6], and quantum metrology [7]. In addition, quantum engineering within the Hilbert space of atomic CSEs is of fundamental interest, as it allows one to explore the isomorphism with the Hilbert space of a single electromagnetic mode [8]. So far, engineering of CSEs has been limited to squeezed spin states [9,10,15] and the single-quantum state [11,12].The single CSE quantum can be prepared by heralding on detection of a photon that has undergone Raman scattering from an atomic ensemble, according to the idea of Duan, Lukin, Cirac and Zoller (DLCZ) [5]. The Hamiltonian governing the Raman scattering event is identical to that of SPDC, leading to the production of a two-mode squeezed state of the scattered light and the CSE. While DLCZ utilizes only the first-order term of the evolution under this Hamiltonian, higher-order terms can be used in combination with complex measurements on the scattered optical mode to produce arbitrary quantum CSE states akin to Bimbard et al. [13].Once the desired collective state has been produced, it needs to be measured. To that end, the readout stage of the DLCZ protocol may be used, in which the CSE is converted into the optical domian in a manner similar to readout from a quantum optical memory based on electromagnetically-induced transparency [14]. Full information about the retrieved optical state, and hence about the CSE, can then be acquired using optical homodyne tomography. An alternative technique of performing tomography on atomic CSEs involves off-resonant Faraday interactions [15].This outlines an approach to synthesis and measurement of arbitrary quantum states of atomic CSEs. Here we present a proof-of-principle experiment to demonstrate the validity of this approach. We produce a heralded single photon from a transient CSE in an atomic vapor cell. For the first time for a photon from an atomic source, we perform homodyne tomography thereupon, obtaining unprecedented uncorrected measurement efficiency of about 50%, leading to a Wigner function which reaches a zero value at the origin of the phase space. In this way, our experiment completes the toolbox required for complete atomic state engineering.Aside from this fundamental aspect, our setup can be viewed as a highly-efficient, spectrally bright source of single photons for experiments on interfaci...

We measure the dispersion relation, gap, and magnetic moment of a magnon in the ferromagnetic F = 1 spinor Bose-Einstein condensate of (87)Rb. From the dispersion relation we measure an average effective mass 1.033(2)(stat)(10)(sys) times the atomic mass, as determined by interfering standing and running coherent magnon waves within the dense and trapped condensed gas. The measured mass is higher than theoretical predictions of mean-field and beyond-mean-field Beliaev theory for a bulk spinor Bose gas with s-wave contact interactions. We observe a magnon energy gap of h × 2.5(1)(stat)(2)(sys) Hz, which is consistent with the predicted effect of magnetic dipole-dipole interactions. These dipolar interactions may also account for the high magnon mass. The effective magnetic moment of -1.04(2)(stat)(8)(sys) times the atomic magnetic moment is consistent with mean-field theory.

Trapped quantum gases can be cooled to impressively low temperatures 1,2 , but it is unclear whether their entropy is low enough to realize phenomena such as d-wave superconductivity and magnetic ordering 3 . Estimated critical entropies per particle for quantum magnetic ordering are ∼0.3k B and ∼0.03k B for bosons in three-and two-dimensional lattices, respectively 4 , with similar values for Néel ordering of latticetrapped Fermi gases 5 . Here we report reliable single-shot temperature measurements of a degenerate Rb gas by imaging the momentum distribution of thermalized magnons, which are spin excitations of the atomic gas. We record average temperatures fifty times lower than the Bose-Einstein condensation temperature, indicating an entropy per particle of ∼0.001k B at equilibrium, nearly two orders of magnitude lower than the previous best in a dilute atomic gas 2,6 and well below the critical entropy for antiferromagnetic ordering of a Bose-Hubbard system. The magnons can reduce the temperature of the system by absorbing energy during thermalization and by enhancing evaporative cooling, allowing the production of low-entropy gases in deep traps.In many experiments on strongly interacting atomic-gas systems, the low-entropy regime is reached by first preparing a weakly interacting bulk Bose gas at the lowest possible temperature, and then slowly transforming the system to become strongly interacting 7-11 . To discern whether the transformation is adiabatic and to determine indirectly the thermodynamic properties of the strongly interacting system, the system is returned to the weakly interacting regime where relations between temperature, entropy and other properties are known. Therefore, methods to lower entropies and measure temperatures of weakly interacting gases are important for the study of both weakly and strongly interacting atomic-gas systems.In this Letter, we report cooling a Bose gas to a few per cent of the condensation temperature, T c , corresponding to an entropy per particle S/N ≈ 1 × 10 −3 k B , where k B is the Boltzmann constant. Surprisingly, we achieve this low entropy using a standard technique: forced evaporation in an optical dipole trap, which we find remains effective in a previously uncharacterized regime. The lowest temperatures we report are achieved at very shallow final trap depths, as low as 20 nK, set by stabilizing the optical intensity with a longterm fractional reproducibility better than 10 −2 . In addition, we demonstrate and characterize a method of cooling that lowers the entropy without changing the trap depth, possibly allowing the lowentropy regime to be reached or maintained in systems where the trap depth is constrained.Both thermometry and cooling require a means of distinguishing thermal excitations. For example, forced evaporative cooling 12,13 depends on the ability to selectively expel high-energy excitations from the system. Similarly, thermometry of a degenerate quantum gas requires one to identify the excitations that distinguish a zero-temperature from...

Precise information about the temporal mode of optical states is crucial for optimizing their interaction efficiency between themselves and/or with matter in various quantum communication devices. Here we propose and experimentally demonstrate a method of determining both the real and imaginary components of a single photon's temporal density matrix by measuring the autocorrelation function of the photocurrent from a balanced homodyne detector at multiple local oscillator frequencies. We test our method on single photons heralded from biphotons generated via four-wave mixing in an atomic vapor and obtain excellent agreement with theoretical predictions for several settings. Keywords: autocorrelation matrix; polychromatic optical heterodyne tomography; single photon; temporal mode function INTRODUCTIONSingle photons and single photon qubits are among the foundations of most quantum optical information processing techniques such as cryptography, 1 teleportation, 2 repeaters 3 and computing. 4 Many of these applications require the photons to have a well-defined, pure modal structure. Possessing precise information about that structure is essential for quantum optical technology.An approximate guess of a photon's mode can be inferred theoretically from the characteristics of the source, 5-9 but this information is not always available or reliable. For example, this approach would not work for photons sent in by a remote party in a communication scheme, or for photons from an incompletely characterized mesoscopic source. Therefore, it is important to have a technique for precise characterization of a photon's mode experimentally. While such techniques are relatively well developed for spatial modes, 10,11 their extension into the temporal domain is challenging.One approach to studying the temporal structure of the photon would be to look at the photon detection event statistics as a function of time. For example, this approach has been used to study the timing of coherent double Raman scattering from an atomic ensemble. 12 Further insight into the photon preparation quality can be gained by studying time-dependent photon counting autocorrelation statistics. 13 However, these techniques provide no information about the phase coherence between different segments of the photon's temporal mode.Complete information about a photon's temporal properties can be obtained by studying its interference with a classical field. Polycarpou et al. used adaptive waveform shaping of local oscillator (LO) pulses 14 to heuristically find the LO temporal mode that maximizes the efficiency of homodyne detection of the photon. This occurs when the LO temporal mode matches that of the signal, enabling measurement of that mode. However, physical shaping of LO pulses is quite sophisticated experimentally. Furthermore, this technique has only been demonstrated for pure temporal modes.An alternative approach to measuring the spectral density matrix of the photon has been proposed in Ref.15. It is based on bringing the photon into interference ...

We present a versatile, inexpensive and simple optical phase lock for applications in atomic physics experiments. Thanks to all-digital phase detection and implementation of beat frequency pre-scaling, the apparatus requires no microwave-range reference input, and permits phase locking at frequency differences ranging from sub-MHz to 7 GHz (and with minor extension, to 12 GHz). The locking range thus covers ground state hyperfine splittings of all alkali metals, which makes this system a universal tool for many experiments on coherent interaction between light and atoms.

The multi-mode character of quantum fields imposes constraints on the implementation of highfidelity quantum gates between individual photons. So far this has only been studied for the longitudinal degree of freedom. Here we show that effects due to the transverse degrees of freedom significantly affect quantum gate performance. We also discuss potential solutions, in particular separating the two photons in the transverse direction.