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Journal of the Optical Society of America B

Ancilla-free scheme for the photon-addition operation and its application to squeezing and coherence manipulation

Muhammad Idrees, Shengli Zhang

Published Aug 26, 2024• 2 citations
Publisher

Abstract

The photon-addition operation is the inverse of the photon-subtraction operation and has many important applications in research on photon number statistics in quantum optics. In this study, we propose a scheme for a photon-addition operation with ancilla-free photonic manipulation. This is in strong contrast to conventional photon-addition operations in which a single-photon ancilla is an indispensable resource for photon addition. Moreover, our scheme helps break the exponential decay trend in the probability of success for photon addition operating in large Fock states. Thus, our scheme can be considered as a useful tool for manipulating the photon number of a bright coherent state or a strongly squeezed state in the near future. To be precise, we used the SU(1,1) beamsplitter to replace the conventional beamsplitter, and our work can be considered another important application of the SU(1,1) beamsplitter. The photon-addition operation is applied to both single- and two-mode quantum entangled states, and our results show that SU(1,1)-based photon addition is more powerful and efficient in terms of the fidelity and success probability of the photon-addition operation.

DOI
10.1364/josab.527260

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The photon-addition operation is the inverse of the photon-subtraction operation and has many important applications in research on photon number statistics in quantum optics. In this study, we propose a scheme for a photon-addition operation with ancilla-free photonic manipulation. This is in strong contrast to conventional photon-addition operations in which a single-photon ancilla is an indispensable resource for photon addition. Moreover, our scheme helps break the exponential decay trend in the probability of success for photon addition operating in large Fock states. Thus, our scheme can be considered as a useful tool for manipulating the photon number of a bright coherent state or a strongly squeezed state in the near future. To be precise, we used the SU(1,1) beamsplitter to replace the conventional beamsplitter, and our work can be considered another important application of the SU(1,1) beamsplitter. The photon-addition operation is applied to both single- and two-mode quantum entangled states, and our results show that SU(1,1)-based photon addition is more powerful and efficient in terms of the fidelity and success probability of the photon-addition operation.
The statistics of photon-subtracted and photon-added states has several important applications in quantum optics and quantum information science. In this study, we propose a scheme for a photon-subtraction operation with SU(1,1) beam splitters. We demonstrate that our scheme overcomes the exponential decaying trend of fidelity and works exceptionally well for quantum states with a large number of photons. Moreover, our scheme is effective even with realistic on-off photon detectors and the heralded single-photon source. Thus, our scheme can serve as a useful tool for manipulating the number of photons in bright coherent states and strongly squeezed states in the future.
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Photon subtraction (PS) is an important operation for optic quantum information processing. Conventional PS is implemented using a single linear beam splitter (BS) and photon detector. However, in this study, we show that the PS effect can be enhanced using two beam splitters and an optional phase modulator. This can be considered PS with an extended version of the well-known Mach–Zehnder (MZ) interferometer. By tuning the transmittance of the two beam splitters and phase modulator, the probability of success can be considerably improved over that of the original PS scheme with a single BS and photon detector. Moreover, if applied to a single-photon input, our proposed scheme can even implement deterministic PS, which is almost impossible for the original scheme with a single BS and photon detector. Owing to the higher probability of success, applying the PSMZ method to the entanglement enhancement of a very weak two-mode squeezed vacuum state is straightforward. Our result is helpful for improving the yield of output entanglement.
We study how photon addition and subtraction can be used to generate squeezed superpositions of coherent states (SSCSs) in free-traveling fields with high fidelities and large amplitudes. It is shown that an arbitrary NNN-photon subtraction results in the generation of a SSCS with nearly the perfect fidelity (F>0.999)(F>0.999)(F>0.999) regardless of the number of photons subtracted. In this case, the amplitude of the SSCS increases as the number of the subtracted photons gets larger. For example, two-photon subtraction from a squeezed vacuum state of 6.1dB6.1\phantom{\rule{0.3em}{0ex}}\mathrm{dB}6.1dB can generate a SSCS of $\ensuremath{\alpha}=1.26$, while in the case of the four-photon subtraction a SSCS of a larger amplitude $\ensuremath{\alpha}=1.65$ is obtained under the same condition. When a photon is subtracted from a squeezed vacuum state and another photon is added subsequently, a SSCS with a lower fidelity $(F\ensuremath{\approx}0.96)$ yet higher amplitude $(\ensuremath{\alpha}\ensuremath{\approx}2)$ can be generated. We analyze some experimental imperfections including inefficiency of the detector used for the photon subtraction.
Photon subtraction and addition are essential non-Gaussian processes in quantum optics, where conventional methods using linear optics and number-resolving detection often suffer from low success probability. Here, we introduce the concept of \textit{dynamic stimulated emission}, whereby a quantum emitter undergoes stimulated emission with a time-dependent coupling. Despite interacting with a multimode photon field, we show that, for both two- and three-level emitters, their dynamics can mimic that of a single-mode Jaynes-Cummings model. This feature can be used to deterministically add or subtract a photon while maintaining a single propagating optical mode. We provide semi-analytic solutions to this problem for Fock states, enabling deterministic and unconditional photon addition and subtraction with fidelity F>0.996{\cal F}>0.996F>0.996. Our semi-analytic solutions are provided for both dynamically coupled two-level systems and for three-level systems whose dynamical coupling is controlled by a coherent laser drive. Moving beyond individual Fock states, we further showcase the ability to subtract and add single photons to photon-number superposition states. We show that Schr{ö}dinger cat states can be prepared from squeezed vacuum input via cascaded subtraction or cascaded addition. Finally, we show that our photon-addition process can be used to add a photon to any squeezed and displaced state with high success probability and fidelity F>0.99{\cal F}>0.99F>0.99, thereby potentially converting quantum emitters from single-photon sources to sources of single-photon-added Gaussian states without the need for inline squeezing. Our protocols provide a path towards integrating quantum emitters to construct efficient sources of single-mode non-Gaussian light beyond single photons.
Photon subtraction (PS), due to its feasibility in physical implementation, has been widely utilized in Gaussian entanglement distillation. However, in this paper, we will show that photon addition (PA) can be employed to provide an additional enhancement in both the quality of distilled entanglement and the success probability if the input state is a weak two-mode squeezed vacuum state. Moreover, compared with biside PS, the distillation probability gains a $O(\frac{1}{{\ensuremath{\lambda}}^{2}})$ improvement, which increases rapidly when $\ensuremath{\lambda}\ensuremath{\ll}1$. Our PA-based scheme is obtained first by single-photon injection and later by vacuum state projection. The performance of PA in the presence of both an approximated single photon and amplitude-damping noise has been analyzed. Our result sheds more light on the indispensable non-Gaussian ingredients in Gaussian-state distillation and could be of great use in developing more efficient distillation schemes. Finally, the sensitivity of the PA scheme to inefficient photon detection has also been investigated.