This thesis presents the results of four
experiments related to applications
of higher dimensional photonic
entanglement. 1) We use energy-time entangled
biphotons from
spontaneous parametric down-conversion (SPDC) to implement a
large-alphabet quantum key distribution (QKD) system which securely
transmits
up to 10 bits of the random key per photon. An advantage
over binary alphabet
QKD is demonstrated for quantum channels with
a single-photon transmissionrate
ceiling. The security of the QKD
system is based on the measurable reduction
of entanglement in the
presence of eavesdropping. 2) We demonstrate the
preservation of
energy-time entanglement in a tunable slow-light medium. The
fine-structure resonances of a hot Rubidium vapor are used to slow
one photon
from an energy-time entangled biphoton generated with
non-degenerate SPDC.
The slow-light medium is placed in one arm of
a Franson interferometer. The observed
Franson fringes witness the
presence of entanglement and quantify a delay
of 1.3 biphoton
correlation lengths. 3) We utilize holograms to discriminate
between
two spatially-coherent single-photon images. Heralded
single photons are
created with degenerate SPDC and sent through
one of two transmission masks
to make single-photon images with no
spatial overlap. The single-photon images
are sent through a
previously prepared holographic filter. The filter discriminates
the single-photon images with an average confidence level of 95%.
4) We employ
polarization entangled biphotons generated from
non-collinear SPDC to violate
a generalized Leggett-Garg
inequality with non-local weak measurements. The
weak measurement
is implemented with Fresnel reflection of a microscope coverslip
on one member of the entangled biphoton. Projective measurement
with computer-controlled polarizers on the entangled state after
the weak measurement
yields a joint probability with three degrees
of freedom. Contextual values
are then used to determine
statistical averages of measurement operations from
the joint
probability. Correlations between the measured averages are shown
to
violate the upper bound of three distinct two-object
Leggett-Garg inequalities
derived from assumptions of
macro-realism. A relationship between the violation
of two-object
Leggett-Garg inequalities and strange non-local weak values is
derived and experimentally demonstrated.
This thesis presents the results of four
experiments related to applications
of higher dimensional photonic
entanglement. 1) We use energy-time entangled
biphotons from
spontaneous parametric down-conversion (SPDC) to implement a
large-alphabet quantum key distribution (QKD) system which securely
transmits
up to 10 bits of the random key per photon. An advantage
over binary alphabet
QKD is demonstrated for quantum channels with
a single-photon transmissionrate
ceiling. The security of the QKD
system is based on the measurable reduction
of entanglement in the
presence of eavesdropping. 2) We demonstrate the
preservation of
energy-time entanglement in a tunable slow-light medium. The
fine-structure resonances of a hot Rubidium vapor are used to slow
one photon
from an energy-time entangled biphoton generated with
non-degenerate SPDC.
The slow-light medium is placed in one arm of
a Franson interferometer. The observed
Franson fringes witness the
presence of entanglement and quantify a delay
of 1.3 biphoton
correlation lengths. 3) We utilize holograms to discriminate
between
two spatially-coherent single-photon images. Heralded
single photons are
created with degenerate SPDC and sent through
one of two transmission masks
to make single-photon images with no
spatial overlap. The single-photon images
are sent through a
previously prepared holographic filter. The filter discriminates
the single-photon images with an average confidence level of 95%.
4) We employ
polarization entangled biphotons generated from
non-collinear SPDC to violate
a generalized Leggett-Garg
inequality with non-local weak measurements. The
weak measurement
is implemented with Fresnel reflection of a microscope coverslip
on one member of the entangled biphoton. Projective measurement
with computer-controlled polarizers on the entangled state after
the weak measurement
yields a joint probability with three degrees
of freedom. Contextual values
are then used to determine
statistical averages of measurement operations from
the joint
probability. Correlations between the measured averages are shown
to
violate the upper bound of three distinct two-object
Leggett-Garg inequalities
derived from assumptions of
macro-realism. A relationship between the violation
of two-object
Leggett-Garg inequalities and strange non-local weak values is
derived and experimentally demonstrated.
The quantum description of light offers a unique set of optical effects that has led to promising applications beyond those described by classical physics. Although well-defined quantum states of light do not persist in typical classical environments, phenomena such as entanglement often enhance optical approaches to communication, measurement, and sensing. With the emergence of new tasks in classical and quantum optical technology, new tools are required that must be specifically engineered including the generation of quantum states. This thesis is concerned with three principle tasks in engineering and implementing entangled photonic states. First, the use of frequency anti-correlated and polarization entangled two-photon states generated during spontaneous parametric down conversion (SPDC) to precisely evaluate optical delays with quantum interferometry is demonstrated in a realistic commercially available optical telecommunication device. Second, the study of correlated orbital angular momentum (OAM) states for efficient object identification is presented. Finally, experimental efforts towards the development of sources for entangled weak coherent states are discussed. The generation of broadband entangled states leading to well-defined second order interference patterns is a necessary step for the application of low coherence quantum interferometry as a metrological device. The flexibility of non-uniformly chirped periodically poled nonlinear crystals offers a rich set of tools for precise state engineering. The experimental evaluation of a broadband source of polarization entanglement is presented. In addition, design considerations for applications that require optimized quantum interference features are discussed along with a numerical investigation of the limits of quantum interferometry with even order dispersion cancellation. We present an experimental demonstration of correlated OAM sensing exploiting the two-dimensional and correlated nature of states produced during SPDC projected onto the OAM basis. Efficient object recognition through the identification of azimuthal symmetries of arbitrary objects is achieved by observing the full two-photon joint OAM spectrum and focusing on non-conserved OAM components not found in the natural OAM spectrum of SPDC. Finally, quantum key distribution (QKD) is currently the most successful quantum optical application; however, a limiting trade off between the achievable rates and distances confines the approach to niche applications. The generation of entangled coherent states has been proposed to transition QKD into a new regime that would set aside single photons and two-photon entangled states for higher intensity coherent pulses. The key technical limitation that has prohibited the demonstration of such states is a reliable source of single-photon cross phase modulation. The plausibility and experimental efforts towards creating such an environment in a solid state device is presented.
The creation and manipulation of biphotons is important for many applications in quantum optics and quantum information. Topics that benefit from efficient biphoton sources range from the most fundamental quantum science experiments to the highly applied fields of quantum communication and quantum computation. Biphoton sources have long been hailed as one of the leading methods for creating entangled photon pairs for tests of Bell's inequality, creating heralded photon pairs that are used in on-demand single-photon sources and heralded measurement techniques, and for quantum communication protocols to name a few. Specifically for quantum communication, biphoton sources are commonly used for cutting edge quantum key distribution (QKD) protocols. In the first part of the thesis, I focus on realizing an efficient biphoton source that produces high yield photon pairs. More specifically, I develop an optimized biphoton source using the nonlinear optical process of spontaneous parametric down-conversion in a second-order nonlinear crystal. I develop a formalism for predicting the two important metrics of a biphoton source: the heralding efficiency and joint count rate. I show how, from a large parameter space, one can tailor the phase matching of the nonlinear interaction to create a high quality biphoton source that produces both high heralding efficiency and high joint count rate. I achieve heralding efficiencies of 86$\\pm5\\%$ and joint count rates of 2.58$\\pm0.6kHzpermWpumppower.Ishowthatusingacollinearnondegenerategeometryallowsforheraldingefficienciesofupto99.7\\%$ assuming no loss in the system. I verify the theoretical model with experimental results and find good agreement. In the second part of the thesis I turn to manipulating the single photons born from the biphoton source for applications in creating single-photon spectrometers and time-frequency QKD systems. The security of QKD is only guaranteed if the two parties have access to a set of states called mutually unbiased states. I create a set of these states in time and their conjugate states in the frequency basis and show that I can manipulate single photon correlations in time and frequency so that an eavesdropper can be detected if she localizes a photon to a 1 ns time interval. Additionally, in these experiments, I stretch a single photon wavepacket of 5-ps-width to a wavepacket of 8.3-ns-width and subsequently recompress it to at least the resolution of the detectors (sim 300 ps). This demonstrates a stretch factor of >1600 for a single-photon pulse using a group velocity dispersive material. To my knowledge, this is the largest reported stretch factor for a single-photon wavepacket produced by a biphoton source. The ability to stretch and recompress a single photon by this amount has applications in creating high-resolution, high-efficiency, single-photon spectrometers as well as advancing time-frequency QKD systems and other temporal pulse shaping applications.
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.
∗ both authors contributed equally Quantum entanglement, the non-separability of a multipartite wave function, became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demon-strated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. With the discovery of spontaneous parametric down-conversion (SPDC) in nonlinear crystals, an efficient source for entangled photon pairs, so-called biphotons, be-came available. It has recently been shown that SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional spatial dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional (1D) arrays can be simulated through classical optical beam propagation in a two-dimensional (2D) photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-type inequality. PACS numbers: 42.50.-p, 42.82.Et, 42.65.Lm
Entanglement and encoding in discrete frequency bins – essentially a quantum analogue of wavelength-division multiplexing – represents a relatively new degree of freedom for quantum information with photons. In this talk I discuss biphoton frequency combs, generated either by spontaneous four-wave mixing (SFWM) from on-chip microring resonators or by spectral filtering of spontaneous parametric down conversion (SPDC) in second order nonlinear crystals. Potential advantages include generation of high dimensional units of quantum information (qudits), which can carry multiple qubits per photon, robust transmission over fiber, and frequency parallelism and routing. Since the initial experiments 2-3 years ago, frequency bin quantum photonics has been advancing rapidly [1, 2]. In this talk I will give special attention to high dimensional entanglement. One of the interesting possibilities is to perform mixing of multiple frequency bins in a single operation, going well beyond nearest neighbor “interactions.” In this vein I will comment on two recent experiments in our lab, each involving more than a dozen frequency bins. One experiment focuses on quantum walks of frequency entangled photon pairs, in which the input state can be coherently steered toward either correlated or anticorrelated quantum walk behavior [3]. In the second case, we show that high-dimensional frequency bin entanglement enables measurement of signal-idler delay at the few picosecond level, ~30× faster than the single photon detectors employed [4].
We generalize the derivation of Leggett-Garg inequalities to systematically treat a larger class of experimental situations by allowing multiparticle correlations, invasive detection, and ambiguous detector results. Furthermore, we show how many such inequalities may be tested simultaneously with a single setup. As a proof of principle, we violate several such two-particle inequalities with data obtained from a polarization-entangled biphoton state and a semiweak polarization measurement based on Fresnel reflection. We also point out a nontrivial connection between specific two-party Leggett-Garg inequality violations and convex sums of strange weak values.