type-II Parametric Down-conversion Research Articles

Partial Bell-State Measurement with Type-II Parametric Down Conversion: Extracting Phase Information from the Zeropoint Field (I).

In this paper, the nexus between the Bell-state measurement and extracting phase information from the zeropoint field is investigated. For this purpose, the Wigner representation in the Heisenberg picture is applied in a Bell-type experiment in which the polarisation-entangled photon pairs generated in a type-II parametric down-conversion do not overlap. The signal intensities at the detectors are calculated in a four-mode approximation, being expressed as functions of the modules and phases of the four zeropoint amplitudes entering the crystal. A general criterion for identifying the correlated detectors is proposed based on the equality of the signal intensities, and without involving the calculation of the joint detection probabilities. In addition, from the analyses in the rectilinear and diagonal basis, it is shown that the distinguishability of the polarisation Bell states, which is in direct correspondence with the joint detection events in each experiment, can be related to the knowledge of the phases of the vacuum field entering the entanglement source, and giving rise to correlated detections. To this purpose, it is conjectured that a detection event is associated with a maximum value of the signal intensity averaged in the modules of the zeropoint amplitudes, as a function of the vacuum phases.

Experimental simulation of spin-1 states by second-order type-II parametric down-conversion

In this paper, by using the second-order parametric down-conversion of the nonlinear crystal, the spin-1 state is simulated by the two-photon polarization entangled modes. Through adjusting the laser pulse power density, the efficiency of second-order parametric down-conversion is enhanced. The intensity of the spin-1 state is 0.5/s. The fidelity of the state is up to F=0.891±0.002, and the contrast is C=17.3. The results provide a new method for Stern-Gerlach measurement on the spin-1 system.

Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics.

We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy. The method allows us to reliably infer the squeezing of genuine two-mode states without any phase reference.

Theory of filtered type-II parametric down-conversion in the continuous-variable domain: Quantifying the impacts of filtering

Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single-photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behavior. A rigorous theoretical description to accurately describe the effects of filtering on PDC, however, is still missing. To date, the theoretical models of filtered PDC are rooted in the discrete-variable domain and only account for filtering in the low gain regime, where only a few photon pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and put forward a simple model, which is able to accurately describe the effects of filtering on PDC in the continuous-variable domain. This developed straightforward theoretical framework enables us to accurately quantify the trade-off between suppression of higher-order modes, reduced purity and lowered Einstein-Podolsky-Rosen (EPR) entanglement, when narrowband filters are applied to multimode type-II PDC.

Theory of quantum frequency conversion and type-II parametric down-conversion in the high-gain regime

Frequency conversion (FC) and type-II parametric down-conversion (PDC) processes serve as basic building blocks for the implementation of quantum optical experiments: type-II PDC enables the efficient creation of quantum states such as photon-number states and Einstein–Podolsky–Rosen (EPR)-states. FC gives rise to technologies enabling efficient atom–photon coupling, ultrafast pulse gates and enhanced detection schemes. However, despite their widespread deployment, their theoretical treatment remains challenging. Especially the multi-photon components in the high-gain regime as well as the explicit time-dependence of the involved Hamiltonians hamper an efficient theoretical description of these nonlinear optical processes. In this paper, we investigate these effects and put forward two models that enable a full description of FC and type-II PDC in the high-gain regime. We present a rigorous numerical model relying on the solution of coupled integro-differential equations that covers the complete dynamics of the process. As an alternative, we develop a simplified model that, at the expense of neglecting time-ordering effects, enables an analytical solution. While the simplified model approximates the correct solution with high fidelity in a broad parameter range, sufficient for many experimental situations, such as FC with low efficiency, entangled photon-pair generation and the heralding of single photons from type-II PDC, our investigations reveal that the rigorous model predicts a decreased performance for FC processes in quantum pulse gate applications and an enhanced EPR-state generation rate during type-II PDC, when EPR squeezing values above 12 dB are considered.

The biaxial nonlinear crystal BiB_3O_6 as a polarization entangled photon source using non-collinear type-II parametric down-conversion

We describe the full characterization of the biaxial nonlinear crystal BiB3O6 (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated beta-BaB2O4 (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by more than three times. Such an improvement is currently required for the generation of multiphoton entangled states.

Spatiotemporal structure of biphoton entanglement in type-II parametric down-conversion

We investigate the spatiotemporal structure of the biphoton correlation in type-II parametric down-conversion (PDC). As in type-I PDC [Phys. Rev. Lett. 102, 223601 (2009)], we find that the correlation is nonfactorizable in space and time. Differently from type I, the type-II correlation in the spontaneous regime displays an asymmetric V-shaped structure in any cross section including time and one transverse dimension. This asymmetry along the temporal coordinate originates from the signal-idler group velocity mismatch and tends to disappear as the parametric gain is raised. We observe a progressive transition toward a symmetric X-shaped geometry similar to that found in type I when stimulated PDC becomes dominant. We also give quantitative evaluations of the localization in space and in time of the correlation, analyze its behavior for different crystal tuning angles, and underline qualitative differences with respect to type-I PDC.

Accessing Higher Order Correlations in Quantum Optical States by Time Multiplexing

We experimentally measured higher order normalized correlation functions (NCF) of pulsed light with a time-multiplexing detector. We demonstrate excellent performance of our device by verifying unity valued NCF up to the eighth order for coherent light and factorial dependence of the NCF for pseudothermal light. We applied our measurement technique to a type-II parametric down-conversion source to investigate mutual two-mode correlation properties and ascertain nonclassicality.

脉冲激光作用下的量子定位实验方案的设计及分析

Based on the principle of quantum coherence and quantum spatial positioning,the experimental scheme of the quantum spatial positioning is designed.The spectrum characteristics of the entanglement photons with spontaneous type-II parametric down-conversion pumped by a broadband frequency pulse laser are discussed.The characteristics of the second-order coherent function and the impact of the phase matching conditions on the quantum spatial positioning are analyzed.It is shown that awith the increase of the pump band-width,the coherence of entangled biphoton is diminished,and the measuring accuracy of the quantum spatial positioning is also reduced.

Two-dimensional characterization of spatially entangled photon pairs

We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down-conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space–momentum entanglement. The role of higher-order spatial modes for observing spatial entanglement between the two photons is discussed.

Multiparameter entangled-state engineering using adaptive optics

We investigate how quantum coincidence interferometry is affected by a controllable manipulation of transverse wave vectors in type-II parametric down-conversion using adaptive optics techniques. In particular, we discuss the possibility of spatial walk-off compensation in quantum interferometry and an effect of even-order spatial aberration cancellation.

Control, measurement, and propagation of entanglement in photon pairs generated through type-II parametric down-conversion

We present a study of the effects of dispersion on the properties of photon pairs generated by type-II collinear spontaneous parametric down-conversion. Specifically, we take into consideration the effects of a chirped pump, as well as of dispersive propagation of the photon pairs. We present expressions for the joint amplitude both in the spectral and temporal domains, as well as for the chronocyclic Wigner function of heralded single photons, which fully characterizes the single-photon spectral (temporal) properties. On the one hand, we show that unwanted effects of pump chirp in terms of the heralded single-photon duration can be suppressed for states designed to be factorable and spectrally elongated. On the other hand, we show that pump chirp constitutes an effective tool for the control of the degree of photon-pair entanglement. We show that when frequency-entangled photon pairs propagate through a dispersive medium, entanglement can ``migrate'' between the modulus and phase of the joint temporal amplitude.

High-sensitivity imaging with multi-mode twin beams

Twin entangled beams produced by single-pass parametric down-conversion (PDC) offer the opportunity to detect weak amount of absorption with an improved sensitivity with respect to standard techniques which make use of classical light sources. We propose a differential measurement scheme which exploits the spatial quantum correlation of type-II PDC to image a weak amplitude object with a sensitivity beyond the standard quantum limit imposed by shot noise. By applying a quantitative numerical model to a specific PDC system (a type-II beta-barium borate crystal), we are able to identify conditions in parameter space suitable for a substantial enhancement of the imaging sensitivity, and we investigate the robustness of this enhancement against experimental imperfections.

Beamlike high-brightness source of polarization-entangled photon pairs

We report on an ultrabright beamlike source of polarization-entangled photon pairs that is suitable for the task of multiphoton quantum information processing. The photon pairs are generated from a beamlike type-II parametric downconversion process in two adjacently located but 180 degrees rotated beta-barium borate crystals. Approximately 30,000 s(-1) entangled photon pairs are recorded experimentally with only 100 mW pump power. The fidelity of the generated entangled state as compared with a Bell state is measured to be 0.974 with the method of quantum state tomography. With this source, we also obtain a violation of Bell's inequality by 61 standard deviations in just a few seconds.

Theory of biphoton generation in a single-resonant optical parametric oscillator far below threshold

We present a quantum-theoretical treatment of biphoton generation in single-resonant type-II parametric down-conversion. The nonlinear medium is continuously pumped and is placed inside a cavity which is resonant for the signal field, but nonresonant for the idler deflected by an intracavity polarizing beam splitter. The intensity of the classical pump is assumed to be sufficiently low in order to yield a biphoton production rate that is small compared to the cavity loss rate. Explicit expressions are derived for the rate of biphoton generation and for the biphoton wave function. The output spectra of the signal and idler field are determined, as well as the second-order signal-idler cross-correlation function which is shown to be asymmetric with respect to the time delay. Due to frequency entanglement in the signal-idler photon pair, the idler spectrum is found to reveal the longitudinal mode structure of the cavity, even though the idler field is not resonant.

Projection measurement of the maximally entangledN-photon state for a demonstration of theN-photon de Broglie wavelength

We construct a projection measurement process for the maximally entangled N-photon state (the NOON-state) with only linear optical elements and photodetectors. This measurement process will give null result for any N-photon state that is orthogonal to the NOON state. We examine the projection process in more detail for N=4 by applying it to a four-photon state from type-II parametric down-conversion. This demonstrates an orthogonal projection measurement with a null result. This null result corresponds to a dip in a generalized Hong-Ou-Mandel interferometer for four photons. We find that the depth of the dip in this arrangement can be used to distinguish a genuine entangled four-photon state from two separate pairs of photons. We next apply the NOON state projection measurement to a four-photon superposition state from two perpendicularly oriented type-I parametric down-conversion processes. A successful NOON state projection is demonstrated with the appearance of the four-photon de Broglie wavelength in the interference fringe pattern.

Distinguishing four photons in an entangled state from two independent pairs of photons

We analyze in a multimode model a recent scheme [Tsujino et al., Phys. Rev. Lett. 92, 153602 (2004)] to distinguish entangled four-photon polarization state from two independent polarization entangled pairs of photons in a single type-II parametric down-conversion process. The fraction of the four-photon entangled state among the two detected photon pairs is found to be related to a quantity that is responsible for the temporal mode match between the photon pairs. A comparison with the single mode models is discussed.

Spatial antibunching of photons with parametric down-conversion

The theoretical framework behind a recent experiment by Nogueira et al. [Phys. Rev. Lett. 86, 4009 (2001)] of spatial antibunching in a two-photon state generated by collinear type-II parametric down-conversion and a birefringent double slit is presented. The fourth-order quantum correlation function is evaluated and shown to violate the classical Schwarz-type inequality, ensuring that the field does not have a classical analog. We expect these results to be useful in the rapidly growing fields of quantum imaging and quantum information.

Multiparameter entanglement in femtosecond parametric down-conversion

A theory of spontaneous parametric down-conversion, which gives rise to a quantum state that is entangled in multiple parameters, such as three-dimensional wavevector and polarization, allows us to understand the unusual characteristics of fourth-order quantum interference in many experiments, including ultrafast type-II parametric down-conversion, the specific example illustrated in this paper. The comprehensive approach provided here permits the engineering of quantum states suitable for quantum information schemes and new quantum technologies.

High-intensity pulsed source of space-time and polarization double-entangled photon pairs

Two spatially separated type-I nonlinear crystals are pumped by femtosecond laser pulses to create entangled photon pairs in the process of spontaneous parametric down-conversion. The two-photon entangled state exhibits high-visibility quantum interference for both polarization and space-time variables without the need of stringent spectral postselection by using narrow-band filters. The visibility is insensitive to the thickness of the crystals, unlike in the case of pulse pumped type-II parametric down-conversion; therefore the intensity can be easily increased by using thick nonlinear crystals. This method will be indispensable in experiments that require a pulsed source of entangled photon pairs, such as generation of multiphoton entangled states, quantum teleportation, and quantum communications.