simulation of open quantum system dynamics using different ......a b c d a b d c simulation of open...

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Simulationofopenquantumsystemdynamicsusingdifferentdegreesoffreedomoflight

DanielF.Urrego,Juan-RafaelÁlvarez,JeffersonFlórez,OmarCalderón-Losada, JiříSvozilík,MayerlinNuñezandAlejandraValencia

Laboratorio deÓptica Cuántica,Universidaddelos Andes,A.A.4976,Bogota,D.C.,ColombiaE-mail:df.urrego1720@uniandes.edu.co

Introduction

QuantumSystem+Environment ExperimentalSetup

Bibliography[1]Bi-Heng Liu,et.al.“Experimentalcontrolofthetransitionfrommarkovian tonon-markovian dynamicsofopenquantumsystems”.NatPhys,7,931-934,(2011).[2]M.A.NielsenandI.L.Chuang,“QuantumComputationandQuantumInformation,”CambridgeUniversityPress,Cambridge,UK,(2000).[3]JeffersonFlórez,et.al..“Interferenceoftwopulse-likespatialbeamswitharbitrarytransverseseparation”.JournalofOptics,18(12):125201,(2016).[4]L.J.SalazarSerrano,A.Valencia,andJ.P.Torres,“Tunablebeamdisplacer”,Rev.Sci.Instrum.86,033109(2015).

ExperimentalResults

Conclusions

The experiment is performed in 5 steps:1. Light source in which an 808 nm CW laser is coupled into a single mode fiber to

obtain a well-known Gaussian beam. A polarizer is used to set the light withvertical polarization.

2. Environment preparation (removable)is carried out by means of interferenceeffects[3]. It is possible to monitor the environment with the 2𝑓 system

3. Quantumsystempreparationtosettheinitialpolarizationstate.4. Couplingisobtainedbymeansofapolarizationtunablebeamdisplacer

(PTBD)[4].5. Quantumdynamicscharacterizationiscarriedoutbymeansofapolarization

analyzer.

We experimentally present the controlled transition, of an open-quantum system, between Markovian and Non-Markovian dynamics [1]. The polarization of light isused as the system, whereas the environment is represented by the spatial structure of light. The controlled coupling of these two domains is done by a polarizationsensitive tunable beam displacer. Additionally, we present the experimental implementation and theoretical model of a controllable dephasing quantum channel usingthe same photonic variables. Differently, from standard dephasing channels [2], the channel here reported presents a non-standard behavior, in the sense that theevolution of a state, from a pure to a mixed state, shows an oscillatory behavior if tracked in the Bloch sphere

• We simulated different quantum dynamics using photons. In particular, the polarization and transverse momentum of light serve as system and environment,respectively.

• Engineering of the transversal profile of light offered us the possibility to change the dynamics of the system. i.e., the transition from Markovian to non-Markovian.• The dynamics of a quantum system were characterized by the relative entropy, 𝑆(𝑦), fidelity, F(𝑦), and trace distance, D(𝑦).• The characterization of a controlling dephasing channel was realized experimentally

Figure 1.

Predoctoral SchoolonNano&QuantumOpticsLesHouches,France.November2017

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Characterizationofsystemsdynamics

Trace Distance

Fidelity

Relative Entropy

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Where 𝝉𝟏 and 𝝉𝟐 are the magnitude of the Bloch vector of 𝝆-𝟏 and 𝝆-𝟐

Non-MarkovianMarkovian

• Where 𝒚 simulates the temporal variable.

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The experimental results of the dynamics of the quantum system for differentenvironments. The experimental data corresponds to diagonal and anti-diagonal initialpolarization states. The Dots are the experimental data and the solid lines are thetheoretical model.

Studyopenquantumdynamics Characterizationdephasingchannel