We explore the multiparticle transition probabilities in Gaussian unitaries effected by a two-mode Bogoliubov bosonic transformation on the mode annihilation and creation operators. We show that the transition probabilities can be characterized by remarkably simple, yet unsuspected recurrence equations involving a linear combination of probabilities. The recurrence exhibits an interferometric suppression term---a negative probability---which generalizes the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons impinging on a beam splitter of rational transmittance. Unexpectedly, interferences thus originate in this description from the cancellation of probabilities instead of amplitudes. Our framework, which builds on the generating function of the non-Gaussian matrix elements of Gaussian unitaries in Fock basis, is illustrated here for the most common passive and active linear coupling between two optical modes driven by a beam splitter or a parametric amplifier. Hence, it also allows us to predict unsuspected multiphoton interference effects in an optical amplifier of rational gain. In particular, we confirm the newly found two-photon interferometric suppression effect in an amplifier of gain 2 originating from timelike indistinguishability [Proc. Natl. Acad. Sci. 117, 33107 (2020)]. Overall, going beyond standard two-mode optical components, we expect our method will prove valuable for describing general quantum circuits involving Bogoliubov bosonic transformations.
The Hong-Ou-Mandel effect is a paradigmatic quantum phenomenon demonstrating the interference of two indistinguishable photons that are linearly coupled at a 50:50 beam splitter. Here, we transpose such a two-particle quantum interference effect to the nonlinear regime, when two single photons are impinging on a parametric down-conversion crystal. Formally, this transposition amounts to exchanging space and time variables, giving rise to an unknown form of timelike quantum interference. The two-photon component of the output state is a superposition of the incident photons being either transmitted or reborn, that is, replaced by indistinguishable substitutes due to their interaction with the nonlinear crystal. We experimentally demonstrate the suppression of the probability of detecting precisely one photon pair when the amplification gain is tuned to 2, which arises from the destructive interference between the transmitted and reborn photon pairs. This heretofore unobserved quantum manifestation of indistinguishability in time pushes nonlinear quantum interference towards a new regime with multiple photons. Hence, composing this effect with larger linear optical circuits should provide a tool to generate multimode quantum non-Gaussian states, which are essential resources for photonic quantum computers.
This thesis explores the interference of nonclassical states of light, particularly Fock and Gaussian states, in noisy linear interferometers, with applications to quantum information and quantum sensing. Using the phase-space formalism, analytical tools based on generating functions are developed to describe quantum optical interference in a unified way. For multiphoton Fock states, new zero probability events (suppression laws) are identified beyond the previously derived symmetry permutation principle, revealing rich interference structures that is degraded with photon distinguishability. For Gaussian states, the Hafnian-based description of Gaussian Boson Sampling is extended to include partial distinguishability via the overlap matrix of the internal state of the photons. Finally, the link between these interference effects and quantum multiparameter estimation is examined for the simultaneous estimation of phase and loss. This study shows that while probe incompatibility can vanish for optimized non-Gaussian states and some two-mode Gaussian states, at high photon number, measurement incompatibility remains a fundamental constraint even in this limit.
Linear canonical transformations of bosonic modes correspond to Gaussian unitaries, which comprise passive linear-optical transformations as effected by a multiport passive interferometer and active Bogoliubov transformations as effected by a nonlinear amplification medium. As a consequence of the Bloch-Messiah theorem, any Gaussian unitary can be decomposed into a passive interferometer followed by a layer of single-mode squeezers and another passive interferometer. Here, it is shown how to circumvent the need for active transformations. Namely, we provide a technique to simulate sampling from the joint input and output distributions of any Gaussian circuit with passive interferometry only, provided two-mode squeezed vacuum states are available as a prior resource. At the heart of the procedure, we exploit the fact that a beam splitter under partial time reversal simulates a two-mode squeezer, which gives access to an arbitrary Gaussian circuit without any nonlinear optical medium. This yields, in particular, a procedure for simulating with linear optics an extended boson sampling experiment, where photons jointly propagate through an arbitrary multimode Gaussian circuit followed by the detection of output photon patterns.
We examine multiphoton interference with a symmetric
SU(N) beam splitter
SN, an extension of features of the
SU(2) 50/50 beam splitter extended Hong-Ou-Mandel (eHOM) effect, whereby one obtains a zero amplitude (probability) for the output coincidence state (defined by equal number of photons
n/N in each output port), when a total number
n of photons impinges on the
N-port device. These are transitions of the form
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N, where
n=∑i=1Nni, which generalize the Hong-Ou-Mandel (HOM) effect $|1,1\rangle \overset{S_2}{\to}|1,1\rangle $, the eHOM effect $|n_1,n_2\rangle \overset{S_2}{\to}|\tfrac{n_1+n_2}{2},\tfrac{n_1+n_2}{2}\rangle $, and the generalized HOM effect (gHOM)
∣1⟩⊗N→SN∣1⟩⊗N, which have previously been studied in the literature. The emphasis of this work is on illuminating how the overall destructive interference occurs in separate groups of destructive interferences of sub-amplitudes of the total zero amplitude. We develop symmetry properties for the generalized eHOM effect (geHOM)
∣n1,n2,…,nN⟩→SN∣n/N⟩⊗N involving a zero amplitude governed by Perm(
Λ)=0, for an appropriately constructed matrix
Λ(SN) built from the matrix elements of
SN. We develop an analytical constraint equation for Perm
(Λ) for arbitrary
N that allows us to determine when it is zero. We generalize the SU(2) beam splitter feature of central nodal line (CNL), which has a zero diagonal along the output probability distribution when one of the input states is of odd parity (containing only odd number of photons), to the general case of
N=2∗N′ where
N′∈odd.
Abstract The ability of indistinguishable particles to interfere with one another is a core principle of quantum mechanics. The interplay of interference and particles exchange statistics1–4 gives rise to the Hong–Ou–Mandel (HOM) effect5, where the bunching of bosons suppresses two-particle coincidences between the output ports of a balanced beamsplitter. Conversely, fermionic anti-bunching can yield up to a twofold enhancement of coincidences compared to the baseline of distinguishable particles. As such, the emergence of dips or peaks in the HOM effect may appear indicative of the particles’ bosonic/fermionic nature. Here, we demonstrate experimentally that the coincidence statistics of boson pairs can be seamlessly tuned from full suppression to enhancement by an appropriate choice of the observation basis. Our photonic setting leverages birefringent couplers6 to introduce differential dissipation in the photons’ polarization. In contrast to previous work7–9, the mechanism underpinning this unusual behaviour does not act on individual phases accumulated by pairs of particles along specific paths, but instead allows them to jointly evade losses as indistinguishable photons are prevented from inhabiting orthogonal modes. Our findings reveal a new approach to harnessing non-Hermitian settings for the manipulation of multi-particle quantum states and as functional elements in quantum simulation.