PHYSICAL REVIEW A 101, 062109 (2020) Squeezing and slowed quantum decoherence in the double-slit experiment L. S. Marinho , 1, 2 I. G. da Paz , 2 and Marcos Sampaio 3 1 Departamento de Física, Universidade Federal de Pernambuco, Recife, PE, Brazil 2 Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, PI, Brazil 3 Departamento de Física, Universidade Federal do ABC, São Paulo, São Paulo, Brazil (Received 26 March 2020; accepted 21 May 2020; published 17 June 2020) We study the slowing of the decoherence effect in the double-slit experiment by considering an initially correlated Gaussian state. The effects of the decoherence are included in a specific propagator which we use to obtain the density matrix at the detection screen. We calculate the uncertainties in the position and momentum for the density matrix as a function of the decoherence at the detection screen. We show that for a contractive initial state and specific times of propagation the state at the detection screen is squeezed in position in comparison with the standard Gaussian superposition. For this squeezed Gaussian superposition state, we observe that the fringe visibility is more robust to the decoherence in comparison with the standard Gaussian superposition. Then, we calculate the negativity of the Wigner function and study its behavior as a function of the decoherence and correlation parameters at the detection screen. We observe that the negativity decreases more slowly for the squeezed Gaussian superposition. DOI: 10.1103/PhysRevA.101.062109 I. INTRODUCTION Decoherence is a process by which a quantum system undergoes entangling interactions with its environment and thus influences the statistics of future measurements on that system. It is a quantum-mechanical effect in itself, distinct from classical dissipation and stochastic fluctuations [1]. As far as time evolution is concerned, quantum system decoher- ence is characterized by a decoherence time much smaller than the relaxation time that characterizes the system energy loss. Decoherence is an ubiquitous phenomenon in quantum systems and plays a fundamental rôle in conceptual founda- tions of quantum-to-classical transitions as first put forward by Zeh [2] 50 years ago. The concept was further elaborated by Zurek [3–9] and has been applied to different systems [10,11]. Interference phenomena are at the core of quantum me- chanics and yet they are easily destroyed by an environ- ment as well as interparticle interactions which have the effect of hastening decoherence. In a double-slit experiment, environmental degrees of freedom spawn decoherence by continuously monitoring a quantum particle through scat- tering. This results in partial which-path information and reduction of visibility. Indeed, it has been observed that one of the most dominant process for the loss of coherence in the mesoscopic domain is the scattering by air molecules [12]. Diffraction and interference with fullerenes have been performed to study wave-particle duality and quantum-to- classical transition of fullerenes [13–15] in the presence of an environment. Moreover, a Kapitza-Dirac-Talbot-Lau in- terferometer for large molecules was studied for C 60 ,C 70 , C 60 F 36 , and C 60 F 48 in Ref. [16]. Moreover, autolocalization due to emission of thermal radiation is also an obstacle to the appearance of quantum effects in macroscopic objects. Their numerous internal degrees of freedom store energy that can be converted into thermal radiation and thus induce decoherence. Usually the environment is not directly controllable or measurable, turning the decoherence which it may induce into a serious limit for technological applications of quan- tum effects. For instance, in quantum information processing and quantum technology, decoherence is a hurdle that must be restrained. In this sense, for instance, quantum error- correction techniques are employed to stave off decoherence and combat other errors using additional resources such as measurement-based methods and ancillary qubits [17–20] as well as decoherence-free subspaces [21]. Some other mechanisms have been envisaged to protect quantum systems from decoherence. In Ref. [22], a scheme was proposed and demonstrated to protect an entangled sys- tem from decoherence based on the reversibility of weak quantum measurements. Recently, the model of a protective measurement of a qubit interacting with a spin environment during the measurement process has been used to study pro- tective quantum measurement in the presence of an environ- ment and decoherence [23]. It has also been suggested that decoherence effects may be reduced by squeezing the envi- ronmental bath [24,25]. Instead of acting on environmental degrees of freedom, it was argued that a reduction of decoher- ence can be accomplished by acting on the state itself. In this sense, it was shown that by squeezing a superposition state, it undergoes reduced decoherence effects [26]. One of the most sensitive instruments in physics is the Laser Interferometer Gravitational-Wave Observatory (LIGO). In order to improve the performance of one of the detectors, it was proposed to use squeezed states of light into one of the paths of a detector to make the detection of a small difference in the lengths of the two arms of the interferometer easier. This has led to the best broadband sensitivity to gravitational waves and has allowed it to detect about 50% more events than before [27]. 2469-9926/2020/101(6)/062109(10) 062109-1 ©2020 American Physical Society