Our next talk in the series QM Talks@CBPF will be delivered by Alexandre B. Tacla (Glasgow). Alexandre has many interests, and a broad knowledge. In this talk he will tell us about his recent results on how to deal with complex many-body systems in an efficient way.
Note that this week, due to the holiday celebrating the Proclamation of the Republic in Brazil on Wednesday, the talk will be on Monday. See the full info below, and be sure to not miss this talk!
Title: Particle-correlated states: A non-perturbative treatment beyond mean field
Speaker: Alexandre B. Tacla (Glasgow)
Coordinates: room 601C, CBPF. 13.11 (Monday), 16h00
Abstract: Many useful properties of dilute Bose gases at ultralow temperatures are predicted precisely by the (mean-field) product-state Ansatz, in which all particles are in the same single-particle state. However, in situations where particle-particle correlations become important, this technique fails and more sophisticated methods are required. In this talk, I will introduce a new set of states that include quantum correlations nonperturbatively: The particle-correlated state (PCS) of N = l × n particles is derived by symmetrizing the n-fold product of an l-particle quantum state. Quantum correlations of the l-particle state “spread out” to any subset of the N bosons by symmetrization. Specifically, I will present the PCS theory for the ground-state of bosonic systems constructed from a two-particle pure state (l=2) [Phys. Rev. A 96, 023621 (2017)]. In particular, I will show (i) how to simulate PCS efficiently for large systems and (ii) how to calculate analytically the reduced density matrices (correlation functions) directly from the PCS normalization factor. Lastly, I will discuss the efficacy of PCS when applied to the two-site Bose-Hubbard model. The key result is that the PCS Ansatz can faithfully represent the exact ground-state over the entire parameter region from a superfluid to a Mott insulator.
This week we have the pleasure to receive Marcelo F. Santos (UFRJ) as a speaker in our series QM Talks@CBPF. Marcelo and co-authors have recently put in the arXiv an intriguing paper: Photonic Counterparts of Cooper Pairs. This article, already accepted for publication in Physical Review Letters, attracted quite some attention (see here the Nature News feature on the article) for proposing that photons can interact inside a medium in a way very similar to that of electrons in a superconducting material, forming the so-called Cooper pairs. Got interested?! Then do not miss Marcelo’s talk. The info follows:
Title: Photonic Cooper pairs
Speaker: Marcelo F. Santos (UFRJ)
Coordinates: room 601C, CBPF. 08.11, 16h00
Abstract: Photons are the elementary particles of light. Contrary to most particles, photons do not interact directly with each other in vacuum. However, when propagating in a material, e.g. water, photon pairs may interact through the medium. In the Raman effect, for example, it is possible that a photon creates or absorbs a vibrational excitation of the material. In this work, we demonstrate theoretically and experimentally that photon pairs may interact via a virtual vibration, meaning that the energy exchanged in the process does not correspond to a quantum of vibrational energy. The same process occurs in a metal at very low temperatures, where virtual vibrations of the medium create an effective attractive interaction between electrons, forming the so-called Cooper pairs. This phenomenon changes a normal metal into a superconductor – a zero-resistance state. We have shown theoretically and experimentally the analogue of this phenomenon with light, namely an effective photon-photon interaction mediated by a virtual vibration, i.e, a photonic Cooper pair. An important next step is to test how far the analogy with superconductivity extends.
Following with our series of seminars QM Talks@CBPF, the next talk will be given by Thiago Guerreiro (PUC-RJ). Thiago has just returned to Brazil after postdoc and PhD in the group of Nicolas Gisin. In this “welcome back” talk, Thiago will tell us about his recent results and also about his research plans. Be sure to be there!
Title: Table-top high-energy quantum physics
Speaker: Thiago Guerreiro (PUC-RJ)
Coordinates: room 601C, CBPF. 01.11, 16h00
Abstract: Often in history, important measurements and discoveries were preceded by long periods of technical development. Today, fundamental physics may be at the edge of a new exciting age which will exploit the development of so-called quantum technologies. In this talk I will discuss examples of how precise control over quantum matter can lead to new developments in fundamental physics, from gravitational waves to the search for new particles and interactions of nature.
From this Friday (20.10) up to the end of the month we have the pleasure to receive Giuseppe Di Molfeta at CBPF. Giuseppe has many contributions to the topic of quantum walks. More specifically he employs quantum walks to simulate all sort of systems: from neutrino oscillations and Dirac equation, all the way up to gravity! The latter is the subject of the talk he will deliver in the Theory Seminar. See the details below, and be sure to be there!
Title: Quantum walking in curved spacetime
Speaker: Giuseppe Di Molfetta (Université Aix-Marseille )
Coordinates: seminar room 6th floor, CBPF. 25.10, 14h30
Abstract:In the framework of Quantum Simulation, a crucial topic for the exploration of physical situations where experiments are currently hard or impossible to setup (e.g. quantum gravity), Quantum Walks (QW) are increasingly recognized as prominent models. A discrete-time QW is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). We introduce Grouped QWs, a generalization of the usual QWs where (i) the input is allowed a simple prior encoding and (ii) the local unitary coin is allowed to act on larger than usual neighborhoods. In  it was shown that the continuum limit of this class of QWs leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in (1 + 1) curved spacetime . Therefore a certain QW provides us with a unitary discrete toy model of a test particle in curved spacetime, in spite of the fixed background lattice.
Here we take a step further and discretize the coin operator itself, only allowing, as elementary local unitary operator, the identity (no propagation) or the Pauli X operator (full-speed propagation). This discretization has the practical advantage of allowing easier experimental implementation, as well as of being of interest for studying the quantization of the metric. We prove that we can obtain the Dirac equation in the case of constant background metric. We also thoroughly analyze the non-constant metric case showing how, due to a non-differentiability issue in the discrete model, a new term arises in the differential equation, deviating from the usual Dirac equation.
 P. Arrighi, S. Facchini, M. Forets, Quantum Inf. Process. (2016) 15: 3467
 G. Di Molfetta, F. Debbasch, M. E. Brachet, Phys. Rev. A 88.4 (2013): 042301
Next in our series QM Talks@CBPF is a talk by Pedro C. da Silva, PhD student here at CBPF. In this talk Pedro will show some interesting results he got during his stay in Maryland, collaborating with the group of Prof. Stephen P. Jordan. Be sure to be there! Details follow.
Title: Quantum Algorithm for Simulating the Wave Equation
Speaker: Pedro C. da Silva (CBPF)
Coordinates: room 601C, CBPF. 11.10, 16h00
Abstract: We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling in state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell’s equations.
We continue our series of seminars with a talk by Daniel S. Tasca (IF-UFF). Daniel and co-authors have recently performed an experiment where they verify that a coarse graining procedure might break the mutual unbiasedness between conjugate variables. That sounds interesting! To know more about the topic, check out Daniel’s article here, and attend to his talk. See you there.
Title: Mutual Unbiasedness in Coarse-grained Continuous Variables
Speaker: Daniel S. Tasca (IF-UFF)
Coordinates: room 601C, CBPF. 27.09, 16h00
Abstract: The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of “standard” coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.
Next week in our QM Talks@CBPF series we’ll have a talk by Víctor Montenegro, from the Pontificia Universidad Catolica de Chile. Victor holds a postdoc position at the PUC-Chile in the group lead by Miguel Orszag — a group which has contributed a lot to the development of the quantum optics area.
Victor is on vacation in Rio, and he was very kind to contact us and to accept to give a talk at CBPF. See the details of the talk below, and be sure to be there!
Title: Macro-mechanical quantum state superposition via spin post-selection in dispersive systems
Speaker: Víctor Montenegro (PUC- Chile)
Coordinates: room 601C, CBPF. 28.06, 16h00
Abstract: Macroscopic quantum superposition states are fundamental to test the classical-quantum boundary and present suitable candidates for quantum technologies. Although the preparation of such states have already been realized, the existing setups commonly consider external driving and resonant interactions, which might limit scalability for quantum computation purposes. Motivated by these, we present a scheme to prepare non-classical states of a macroscopic mechanical object. The protocol comprises a probabilistic qubit (0 and 1 phononic states) superposition, and the generation of mechanical Schroedinger’s cat states. To realize this, we have considered an open spin-mechanical quantum system via conditional displaced interaction Hamiltonian in the dispersive regime without any need for adjusting resonances. Therefore, in comparison with previous works on the matter, our proposal does not rely on any non-linearity, energy exchange nor external pumping —which could be an advantage for scalability purposes. Our probabilistic preparation protocol is uniquely based on two steps. Firstly, we weakly evolve the spin-mechanical system for a time t, allowing us to truncate the oscillator Hilbert space up to a single phonon excitation. Subsequently, we then proceed to post-select the spin system. The latter step aims to prepare (probabilistically) any mechanical qubit superposition. Our results can be understood within the clear connection between the quantum coherence of the mechanics and the amplification of the position and momentum quadratures on average.