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Temporal coherence in an unbalanced SU(1,1) interferometer

Optics Letters

December 2022
48(1):127-130

DOI:10.1364/OL.470115

Authors:

Nan Huo

Xueshi Guo

Technical University of Denmark

Show all 6 authorsHide

In classical coherence theory, coherence time is typically related to the bandwidth of the optical field. Narrowing the bandwidth by optical filtering will result in the lengthening of the coherence time. In the case of a delayed pulse photon interference, this will lead to pulse overlap and recovery of interference, which is otherwise absent due to time delay. However, this is changed for entangled optical fields. In this Letter, we investigate how the temporal coherence of the fields in a pulse-pumped SU(1,1) interferometer changes with the bandwidth of optical filtering. We find that the effect of optical filtering is not similar to the classical coherence theory in the presence of quantum entanglement. A full quantum theory is presented and can explain the phenomena well.

(a) Experimental setup of the SU(1,1) interferometer. (b) Interference fringe observed when the phase of pump P2 is varied by changing the voltage applied on the PZT. (c) Visibility as a function delay $\Delta _s$ with $\Delta _i =0$ for various filter bandwidth. BS, 50/50 beam splitter; CWDM, coarse wavelength division multiplexer; DSF, dispersion shifted fiber; F1, ${\rm F_s}$ , filter; P1, P2, pump; PA1, PA2, parametric amplifier; PZT, piezoelectric transducer; SPD, single-photon detector; FPC, fiber polarization controller; $\Delta _s, \Delta _i$ , delay.

…

Visibility as a function of reciprocal bandwidth of the filter: (i) $\Delta _i=0$ , $\Delta _s =10$ ps; (ii) $\Delta _i= 5$ ps, $\Delta _s = 10$ ps; (iii) $\Delta _i=\Delta _s = 10$ ps. In the measurement, $1/\sigma _p=3.6$ ps.

…

(a) Plot of $T_i$ as a function of reciprocal bandwidth $1/\sigma _{\rm f}$ of the signal field filter for the pump pulse width of (i) $1/\sigma _p = 2.7$ ps, (ii) $1/\sigma _p= 3.6$ ps, and (iii) $1/\sigma _p= 9$ ps. The solid curves represent the fitting of Eq. (13). As a comparison, T $_s$ is also plotted from Eq. (12) together with measured data, corresponding to $\sigma _p=0$ for $T_i$ . (b) Plot of $\log V$ versus $\Delta _i^2$ for various filter bandwidths at $1/\sigma _p= 3.6$ ps with linear fit for extracting $T_i$ .

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Letter Vol. 48,No. 1 /1 January 2023 / Optics Letters 127

Temporal coherence in an unbalanced SU(1,1)

interferometer

Yunxiao Zhang,1Nan Huo,1Liang Cui,1Xueshi Guo,1Xiaoying Li,1,∗AND Z. Y. Ou2,3

1College of Precision Instrument and Opto-Electronics Engineering, Key Laboratory of Opto-Electronics Information Technology, Ministry of

Education, Tianjin University, Tianjin 300072, China

2Department of Physics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China

3e-mail: jeffou@cityu.edu.hk

*Corresponding author: xiaoyingli@tju.edu.cn

Received 11 July 2022; revised 27 October 2022; accepted 31 October 2022; posted 9 November 2022; published 22 December 2022

In classical coherence theory, coherence time is typically

related to the bandwidth of the optical ﬁeld. Narrowing the

bandwidth by optical ﬁltering will result in the lengthening

of the coherence time. In the case of a delayed pulse photon

interference, this will lead to pulse overlap and recovery of

interference, which is otherwise absent due to time delay.

However, this is changed for entangled optical ﬁelds. In this

Letter, we investigate how the temporal coherence of the

ﬁelds in a pulse-pumped SU(1,1) interferometer changes

with the bandwidth of optical ﬁltering. We ﬁnd that the

eﬀect of optical ﬁltering is not similar to the classical coher-

ence theory in the presence of quantum entanglement. A full

quantum theory is presented and can explain the phenom-

https://doi.org/10.1364/OL.470115

In quantum mechanics, indistinguishability is a fundamental

concept for quantum interference. When there exist distinguish-

able paths for two interfering ﬁelds, no interference can occur.

This is at the heart of Bohr’s complementarity principle for

quantum interference [1]. However, path distinguishability can

be erased by projection measurement in quantum erasers [2,3].

This erasure of distinguishability can also be achieved in the

measurement process. For example, optical ﬁltering can increase

the coherence time of an optical ﬁeld. In an interference experi-

ment involving optical pulses, when optical delay is introduced

to achieve distinguishability in time, no interference occurs by

direct detection. However, placing a narrowband ﬁlter in front of

the detector can erase the temporal distinguishability by length-

ening the pulse and recover the interference eﬀect. This is what

leads to the important concept of coherence time in classical

coherence theory. Coherence time is the time interval in which

an optical ﬁeld keeps its phase correlation and, according to the

classical coherence theory, it is typically related to the reciprocal

bandwidth of an optical ﬁeld [4] and can be lengthened by opti-

cal ﬁltering. Indeed, a Gaussian-shaped ﬁeld passing through

a ﬁlter of Gaussian proﬁle of width σfhas its coherence time

changed from its original Tcto

T′

c=T2

c+1/σ2

f.(1)

However, there exists quantum entanglement for quantum

ﬁelds. The strong quantum correlations between two entangled

ﬁelds can lead to disappearance of interference in one ﬁeld from

the distinguishability of the other [5,6] and recovery of inter-

ference by erasure of this distinguishability through projection

measurement [2,3]. Moreover, it is even possible to remotely

manipulate the coherence property of one ﬁeld by controlling

the other entangled ﬁeld [7]. All this poses a challenge for the

aforementioned traditional concept of coherence time as related

to the reciprocal bandwidth of the ﬁeld.

An SU(1,1) interferometer is an interferometer involving

quantum entanglement, which is a perfect platform for this

study. It uses parametric ampliﬁers (PAs) to replace beam split-

ters in traditional classical interferometers [8,9]. The signal and

idler ﬁelds generated in the PA were shown to be entangled to

each other [7,10,11], and are used to probe phase changes in

the interferometer [12]. Such a novel quantum interferometer

has recently been widely applied to quantum imaging, quantum

sensing, quantum state engineering, and quantum measurement

[7,9,12]. Because of the involvement of two-partite quantum

entanglement in the interferometer, its properties can be quite

diﬀerent from a traditional classical interferometer [12].

In this Letter, we investigate how optical ﬁltering can aﬀect the

performance of an unbalanced pulsed SU(1,1) quantum inter-

ferometer where a recent experiment demonstrated the loss of

interference in direct intensity detection due to temporal distin-

guishability but recovery of interference by homodyne detection

[13]. A question arises naturally about whether an optical ﬁlter

can be placed in front of the detector to recover interference in

direct intensity measurement in the unbalanced SU(1,1) inter-

ferometer, in a similar way to a traditional interferometer. Our

investigation ﬁnds that the eﬀect of optical ﬁltering plays out

diﬀerently under diﬀerent pumping conditions and for delays in

diﬀerent ﬁelds (signal or idler) in the interferometer. We investi-

gate in both theory and experiment what parameters determine

the appearance of interference. Our investigation is useful for the

application of an SU(1,1) interferometer, in which the sample

length makes the two arms between two PAs unequal.

The experimental setup of our SU(1,1) interferometer is

shown in Fig. 1(a). The two parametric ampliﬁers (PA1,PA2)

are based on pulse-pumped four-wave mixing (FWM) in

dispersion-shifted ﬁbers (DSF1, DSF2). PA1 functions as a wave

Corrected 5 January 2023

ResearchGate has not been able to resolve any citations for this publication.

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Temporal coherence in an unbalanced SU(1,1) interferometer

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