Entanglement and state characterisation from two-photon interference

This thesis analyses the effects of two-photon interference in a polarisation squeezed state under two different points of view: on one hand, it presents a new method to obtain the temporal wavefunction of a state of two photons; on the other hand, it studies the microscopic entanglement properties of a collective nonclassical polarisation state, such as the polarisation squeezed state. The complete characterisation of an unknown quantum state often requires complicated reconstruction methods due to its complex nature: in the first part of this thesis, we describe a new technique to recover completely the wavefunction of a state with two photons (a ¿biphoton¿) with just few simple measurements, thanks to the interference with a coherent reference. With this technique, we reconstruct successfully the wavefunction of single-mode biphotons from a low-intensity narrowband squeezed vacuum state. Many large collective systems that feature nonclassical properties, e.g. superconductivity and squeezing, show entanglement among their components at their microscopic level. Here we report the first direct study of this kind of entanglement for light polarisation. In analogy with the spin-squeezing inequalities that connect squeezing to entanglement for atomic ensembles, we derive an inequality valid for states with classical polarisation correlations, whose violation implies pairwise entanglement among the photons in the state. We consider a polarisation squeezed state that results from the combination in the same spatial mode of a squeezed vacuum state, generated by an optical parametric oscillator (OPO), and a coherent state with orthogonal polarisations: we find that this kind of state always violates our inequality within the coherence time of the squeezed vacuum state. We also quantify the entanglement between the photon pairs by computing the concurrence of the two-photon reduced density matrix: we find that the states that exhibit higher entanglement satisfy the condition for higher visibility of the two-photon interference. We also find that the concurrence is larger for lower squeezing levels, in agreement with the monogamy of entanglement and in analogy to the atomic case. This translation of spin-squeezing inequalities to the optical domain enables us to test directly the squeezing-entanglement relationship. We generate a squeezed vacuum state with an OPO and we combine it with a coherent state to generate a polarisation squeezed state and we measure the photon pair counts for different polarisation bases. We recover the density matrices corresponding to different realisations of the polarisation squeezed state via quantum tomography: all the density matrices that we reconstruct with this method are entangled, with concurrence up to 0.7. Our measurements confirm several theoretical predictions, including entanglement of all photon pairs within the squeezing coherence time.En esta tesis se analizan los efectos de la interferencia de dos fotones en un estado comprimido en polarización desde dos puntos de vista: por un lado, se presenta un nuevo método para obtener la función de onda temporal de un estado de dos fotones; por el otro, se estudian las propiedades de entrelazamiento microscópico de un estado colectivo de polarización no clásico, como el estado comprimido en polarización. La completa caracterización de un estado cuántico desconocido requiere frecuentemente métodos de reconstrucción complicados debido a su compleja naturaleza: en la primera parte de esta tesis describimos una nueva técnica para recuperar completamente la función de onda de un estado con dos fotones (un bifotón) usando pocas medidas sencillas, gracias a la interferencia con un estado coherente de referencia. Con esta técnica, reconstruimos con éxito la función de onda de los bifotones que pertenecen a un estado de vacío comprimido de banda estrecha y de baja intensidad. Muchos sistemas colectivos con un gran número de partículas que presentan propiedades no clásicas, como por ejemplo superconductividad y estados comprimidos, muestran entrelazamiento entre sus componentes a nivel microscópico. Aquí describimos el primer estudio directo de este tipo de entrelazamiento para los estados de polarización de la luz. En analogía con las desigualdades para estados comprimidos en espín, derivamos una desigualdad válida para estados con correlaciones clásicas en polarización, cuya violación implica entrelazamiento en parejas entre los fotones del estado. Consideramos un estado comprimido en polarización, que es el resultado de la combinación en el mismo modo espacial de un estado de vacío comprimido generado por un oscilador óptico paramétrico (OPO) y de un estado coherente con polarización ortogonal al primero: hallamos que estos estados violan nuestra desigualdad siempre que nos encontremos dentro del tiempo de coherencia del estado de vacío comprimido. Cuantificamos también el entrelazamiento entre las parejas de fotones calculando la concurrencia de la matriz de densidad reducida de dos fotones: observamos que los estados que tienen mayor entrelazamiento satisfacen la condición para la visibilidad máxima de la interferencia entre bifotones. Hallamos también que la concurrencia es mayor para niveles de compresión menores, en acuerdo con la monogamia del entrelazamiento, siendo este resultado análogo al caso atómico. El trasladar estas desigualdades para los estados comprimidos en espín al dominio óptico nos permite observar directamente la relación entre estados comprimidos y entrelazamiento de manera experimental. Con este fin generamos un estado de vacío comprimido con un OPO y lo combinamos con un estado coherente para obtener un estado comprimido en polarización y contamos las parejas de fotones en diferentes bases de polarización. Con estas medidas reconstruimos las matrices de densidad que corresponden a diferentes versiones del estado comprimido en polarización usando tomografía cuántica: todas las matrices de densidad que hemos obtenido con este método están entrelazadas, mostrando valores de concurrencia de hasta 0.7. Nuestras medidas confirman las predicciones teóricas, entre las que se encuentra el entrelazamiento de todas las parejas de fotones dentro del tiempo de coherencia del estado entrelazado

Atom-Resonant Heralded Single Photons by Interaction-Free Measurement

We demonstrate the generation of rubidium-resonant heralded single photons for quantum memories. Photon pairs are created by cavity-enhanced down-conversion and narrowed in bandwidth to 7 MHz with a novel atom-based filter operating by "interaction-free measurement" principles. At least 94% of the heralded photons are atom-resonant as demonstrated by a direct absorption measurement with rubidium vapor. A heralded auto-correlation measurement shows $g_c^{(2)}(0)=0.040 \pm 0.012$, i.e., suppression of multi-photon contributions by a factor of 25 relative to a coherent state. The generated heralded photons can readily be used in quantum memories and quantum networks.Comment: 5 pages, 4 figure

A macroscopic quantum state analysed particle by particle

Explaining how microscopic entities collectively produce macroscopic phenomena is a fundamental goal of many-body physics. Theory predicts that large-scale entanglement is responsible for exotic macroscopic phenomena, but observation of entangled particles in naturally occurring systems is extremely challenging. Synthetic quantum systems made of atoms in optical lattices have been con- structed with the goal of observing macroscopic quantum phenomena with single-atom resolution. Serious challenges remain in producing and detecting long-range quantum correlations in these systems, however. Here we exploit the strengths of photonic technology, including high coherence and efficient single-particle detection, to study the predicted large-scale entanglement underlying the macroscopic quantum phenomenon of polarization squeezing. We generate a polarization-squeezed beam, extract photon pairs at random, and make a tomographic reconstruction of their joint quantum state. We present experimental evidence showing that all photons arriving within the squeezing coherence time are entangled, that entanglement monogamy dilutes entanglement with increasing photon density and that, counterintuitively, increased squeezing can reduce bipartite entanglement. The results provide direct evidence for entanglement of macroscopic numbers of particles and introduce micro-analysis to the study of macroscopic quantum phenomena

Ultra-Narrow Faraday Rotation Filter at the Rb D1 Line

We present a theoretical and experimental study of the ultra-narrow bandwidth Faraday anomalous dispersion optical filter (FADOF) operating at the rubidium D1 line (795 nm). This atomic line gives better performance than other lines for the main FADOF figures of merit, e.g. simultaneously 71% transmission, 445 MHz bandwidth and 1.2 GHz equivalent noise bandwidth.Comment: 3 pages, 2 figures. Manuscript same as v1. FADOF calculator (ancillary file) now allows for extension to the D2 lin

Entanglement-enhanced probing of a delicate material system

Quantum metrology uses entanglement and other quantum effects to improve the sensitivity of demanding measurements. Probing of delicate systems demands high sensitivity from limited probe energy and has motivated the field's key benchmark-the standard quantum limit. Here we report the first entanglement-enhanced measurement of a delicate material system. We non-destructively probe an atomic spin ensemble by means of near-resonant Faraday rotation, a measurement that is limited by probe-induced scattering in quantum-memory and spin-squeezing applications. We use narrowband, atom-resonant NOON states to beat the standard quantum limit of sensitivity by more than five standard deviations, both on a per-photon and per-damage basis. This demonstrates quantum enhancement with fully realistic loss and noise, including variable-loss effects. The experiment opens the way to ultra-gentle probing of single atoms, single molecules, quantum gases and living cells.Comment: 7 pages, 8 figures; Nature Photonics, advance online publication, 16 December 201

Ultranarrow Faraday Rotation Filter at the Rb D-1 Line

We present a theoretical and experimental study of the ultra-narrow bandwidth Faraday anomalous dispersion optical filter (FADOF) operating at the rubidium D1 line (795 nm). This atomic line gives better performance than other lines for the main FADOF figures of merit, e.g. simultaneously 71 % transmission, 445MHz bandwidth and 1.2GHz equivalent noise bandwidth. c © 2013 Optical Society of America OCIS codes: 020.1335, 010.3640 Ultra-narrow bandwidth optical filters are key el-ements in laser remote sensing (LIDAR), observa-tional astronomy, free-space communications and quan-tum optics. Relative to conventional interference fil-ters, FADOFs offer high background-rejection, mechani-cal robustness, imaging capability and high transmission. FADOFs have been developed for several alkali atom res-onances – Cs D2 [1] and 6S1/2 → 7P3/2 [2] lines, Rb D2 line [3, 4], K (three lines) [5], Na D lines [6], and for Ca [7]. We demonstrate a FADOF on the D1 line of Rb (wave-length 795 nm). This line, efficiently detected with Si detectors, accessible with a variety of laser technolo-gies, and with large hyperfine splittings, is a favorite for coherent and quantum optics with warm atomic va-pors. Applications include electromagnetically-induced transparency [8], stopped light [9], optical magnetom-etry [10, 11], laser oscillators [12], polarization squeez-ing [13, 14], quantum memory [15] and high-coherence heralded single photons [16,17]. Here we show that the Rb D1 line provides supe-rior FADOF performance. We demonstrate a FADOF surpassing other atoms and other Rb transitions for key figures of merit, including peak transmission Tmax, transmission bandwidth and equivalent noise bandwidth ENBW = T−1max T (ν)dν, where T (ν) is the filter trans-mission versus frequency ν [4]

Citizen Science to Assess Light Pollution with Mobile Phones

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).The analysis of the colour of artificial lights at night has an impact on diverse fields, but current data sources have either limited resolution or scarce availability of images for a specific region. In this work, we propose crowdsourced photos of streetlights as an alternative data source: for this, we designed NightUp Castelldefels, a pilot for a citizen science experiment aimed at collecting data about the colour of streetlights. In particular, we extract the colour from the collected images and compare it to an official database, showing that it is possible to classify streetlights according to their colour from photos taken by untrained citizens with their own smartphones. We also compare our findings to the results obtained from one of the current sources for this kind of study. The comparison highlights how the two approaches give complementary information about artificial lights at night in the area. This work opens a new avenue in the study of the colour of artificial lights at night with the possibility of accurate, massive and cheap data collection. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.This work is part of the R&D project CEX2019-000910-S, funded by MCIN/AEI/10.13039/501100011033/, from Fundació Cellex, Fundació Mir-Puig, and from Generalitat de Catalunya through the CERCA program. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 847635 (UNA4CAREER). RALAN map project. This work was supported by the EMISSI@N project (NERC grant NE/P01156X/1). G.M-G. acknowledges support from the Austrian Science Fund (FWF) through SFB BeyondC F7102 and from Fundació LaCaixa. A.D. acknowledges NOQIA; Ministerio de Ciencia y Innovation Agencia Estatal de Investigaciones (PGC2018-097027-B-I00/10.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019-106901GB-I00, FPI, QUANTERA MAQS PCI2019-111828-2, QUANTERA DYNAMITE PCI2022-132919, Proyectos de I+D+I “Retos Colaboración” QUSPIN RTC2019-007196-7); European Union NextGenerationEU (PRTR); Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program (AGAUR Grant No. 2017 SGR 134, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014-2020); Barcelona Supercomputing Center MareNostrum (FI-2022-1-0042); EU Horizon 2020 FET-OPEN OPTOlogic (Grant No 899794); National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314); European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No 101029393 (STREDCH) and No 847648 (“La Caixa” Junior Leaders fellowships ID100010434: LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012, LCF/BQ/PR21/11840013). A.D. further acknowledges the financial support from a fellowship granted by la Caixa Foundation (ID 100010434, fellowship code LCF/BQ/PR20/11770012). Project cofinanced by the Diputació de Barcelona through the BiblioLab program (21296).Peer reviewe