Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.
Generation of multi-photon states (such as for instance three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states testing Bell's inequalities for spin-1 quantum systems preparing W-states and other applications. In this paper we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC or even PDC in the stimulated regime demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime which allows one to study multi-photon correlations for these and many other processes.
Multi-particle entangled states are becoming more and more interesting for different applications in quantum information, such as quantum multi-particle teleportation, entangled based cryptography and quantum communication schemes based on multi-particle states, but also for fundamental reasons such as testing local realism by means of the Greenberger-Horne-Zeilinger states (GHZ) arguments . The advantage of multiparticle entanglement versus the most common two particle one lies in the fact that the greater the number of particles involved in the entangled state, the more clearly the quantum effects are exhibited. Our final goal is to exploit the multi-photon entangled states for quantum metrology. By the interaction of those states with nanostructures (mostly nanoholes, but in a future also nanospheres), we expect to reach sub-wavelength sensitivity phase measurements beating the Standard Quantum Limit as well as to detect plasmonic effects. In this thesis we present our work consisting on designing and building an experimental setup for the generation of states of 4-photon entangled in the transverse linear momentum. In the first part we explain some basics in the form of a technical introduction. We then adapt a general theoretical model to our particular case, explaining the physics of the process of generation of entangled states of photons. We proceed explaining the details of our setup, as well as the procedure of measurement. We then present the results of our tests in a "standard" 2-photon regime to show the correct functioning of the setup itself. Some more sophisticated measurements using structured light in the form of a first-order Hermite-Gaussian mode has been performed to generate entanglement in higher spatial modes are also presented. We conclude with theoretical and experimental details regarding the 4-photon experiments feasible with our setup. Our source is based on Spontaneous Parametric Down-Conversion (SPDC). In the last two decades it has been extensively studied for the generation of two-photon entangled states, since Kwiat et al. published in 1995 the new scheme based on polarization entangled photons. Most of the studies regarding entangled states involving more than two photons are indeed based on quantum correlations in the polarization or in the path of the down converted beams. The great advantage of entangling a spatial degree of freedom (as we do) is related to the dimensionality of the Hilbert space in which the state is defined. In the particular case of linear momentum, which is a continuous variable, we are dealing with infinite dimensions. Since in each dimension of the state one quanta of information can be encoded, the advantage of having multidimension entanglement for the field of quantum communication and computing is clear. The specs of our setup include a periodically-poled KTP crystals offering high conversion efficiency and cut for type-0 SPDC. The photons generated are well known to be inherently entangled in different degrees of freedom such as polarization, energy-time, linear momentum, and orbital angular momentum. Since each single SPDC event generates one photon pair, in order to reach four photon we entangle two consecutive SPDC events per each state. Furthermore, it is possible to manipulate (to enhance) the dimensionality of the entanglement by properly tailoring the pump spatial profile. The key point for the generation of four-photon entangled states is that, under some conditions, two consecutive pairs generated via SPDC cannot be described as two independent pairs but necessarily as a four-photon state showing genuine entanglement. This can happen when using a pulsed laser to generate the entangled photons; in particular, in the regime in which the coherence time of the down-converted photons τc is (much) longer than the temporal length of the pumping pulse Δt. In this condition the emission of a second pair is stimulated by the presence of the first one. That effect can be ultimately seen as a constructive multi-particle interference effect, the deep origin of which has to be sought in the boson statistic of photons.
We propose two interesting methods of generating the four-photon W state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon W state, the three-photon Greenberger–Horne–Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general n -photon W state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.
Nowadays,the generation of multiphoton entangled states is almost realized by combining the coupled entangled photons emitted from spontaneous parametric down-conversion (SPDC) with the first-order term.In this case,one may focus mainly on the first-order term,and then avoid multipair emission events by restricting experimental parameters.On the other hand,for the higher-order terms in SPDC source,these emitted entangled photons have interesting features.For example,they are entangled maximally not only in photon number for the spatial modes,but also in polarization degree of freedom.In general,two photons,which are entangled in two or more degrees of freedom,are called hyperentangled pair of photons or hyperentangled state.We present a scheme to generate the four-photon hyperentangled state based on four indistinguishable photons emitted from SPDC source with the second-order term.Consider two SPDC sources with equal probability of emission of photons in respective spatial modes.With the passive linear optical devices,i.e., beam splitters,half wave plates,polarizing beam splitters,etc.,under the condition of registering a specified four-photon coincidence,we can obtain the four-photon hyperentangled state in which the photons are entangled in both polarization and spatial-mode degrees of freedom.Here,of course,for an arbitrary fourfold coincidence detection,one obtains a canonical four-photon Greenberger-Horne-Zeilinger (GHZ) state.Then we show the results of fourfold coincidence detections and the corresponding probabilities for the four-photon GHZ states,where the generation of the four-photon hyperentangled state is included as long as we are not to distinguish the two detectors located at the same locations. As a result,our scheme has two notable features.When we only consider the second-order emission,since it is not needed for us to distinguish between the two SPDC sources,the present scheme is simple and feasible.Also,based on the postselection with fourfold coincidence detection,our scheme is suitable for the normal first-order emission where we restrict the four photons emitted from the same source.In this sense,our scheme is efficient.In a word,we describe a method to generate the four-photon hyperentangled state with the second-order emission in SPDC source,which may contribute to the exploration of multipair entanglement with higher-order emissions from the SPDC source.
We propose two interesting methods of generating the four-photon W state. These methods use parametric down-conversion processes, linear optical elements, and commercial photon detectors, which are readily feasible under current technology. They can also be used to generate the three-photon W state, the three-photon Greenberger-Horne-Zeilinger state, and the three-photon maximally entangled photon-number state (a typical photon-number entanglement state) by simply changing some experimental components or their parameters. Moreover, assuming we have photon number-resolving detectors, these methods can develop into methods that generate a general n-photon W state. They are expected to become powerful tools for experimental investigations of multipartite entanglement and its applications to quantum information processing.
This article is devoted to the generation and the quantum correlations of triple photons, which correspond to the creation of three highly correlated photons from the splitting of a single photon by a phase-matched third-order parametric nonlinear process. These triples constitute a Greenberger–Horne–Zeilinger state of light and are interesting from a fundamental point of view but also for new schemes of quantum cryptography. We give here the classical and quantum descriptions of triple photon generation, we report on the first experimental demonstration of such a generation, and we calculate the Wigner function of three-photon quantum states of light.
We identify a relation between the number of photon pairs generated by parametric fluorescence, through either spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing, and the number generated by the corresponding stimulated process, respectively, either difference-frequency generation or stimulated four-wave mixing. On the basis of this very general result, we show that the characterization of SPDC sources of two-photon states in a given system can be performed solely by studying stimulated emission. We call this technique stimulated emission tomography (SET). We show that the number of photons detected in SET can be 9 orders of magnitude larger than the average number of coincidence counts in two-photon quantum state tomography. These results open the way to the study of sources of quantum-correlated photon pairs with unprecedented precision and unparalleled resolution.