arXiv:1702.06636 · Physical Review A

Method for generating a photonic NOON state with quantum dots in coupled nanocavities

Kenji Kamide, Yasutomo Ota, Satoshi Iwamoto, Yasuhiko Arakawa

Published Jul 27, 2017• 17 citations

Abstract

We propose a method to generate path-entangled NOON-state photons from quantum dots and coupled nanocavities. In the systems we considered, cavity mode frequencies are tuned close to the biexciton two-photon resonance. Under appropriate conditions, the system can have the target NOON state in the energy eigenstate, as a consequence of destructive quantum interference. The NOON state can be generated by a resonant laser excitation. This method, first introduced for a two-photon NOON state ($N=2$), can be extended toward a higher NOON state ($N>2$) based on our recipe, which is applied to the case of $N=4$ as an example.

DOI: 10.1103/physreva.96.013853

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Publisher's Note: Method for generating a photonic NOON state with quantum dots in coupled nanocavities [Phys. Rev. A 96 , 013853 (2017)]

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arXiv:1702.06636 · Physical Review A

Method for generating a photonic NOON state with quantum dots in coupled nanocavities

Kenji Kamide, Yasutomo Ota, Satoshi Iwamoto, Yasuhiko Arakawa

Published Jul 27, 2017• 17 citations

arXiv HTML PDF

Abstract

N=2

), can be extended toward a higher NOON state (

N>2

) based on our recipe, which is applied to the case of

N=4

as an example.

DOI: 10.1103/physreva.96.013853

Related papers

Generation of two-photon noon state and polarization-entangled state from a single quantum dot embedded inside a microcavity

Jitendra K. Verma, Harmanpreet Singh, Pradyumna K. Pathak

We discuss generation of two types of entangled states of two photons: noon state, which is entangled in number and polarization, and polarization-entangled state, which is entangled in polarization and frequency. We consider a single quantum dot coupled with a bimodal cavity in a strong coupling regime. We analyze the effect of exciton–phonon coupling on concurrence of the generated entangled states. We find that for both states, concurrence is maximum in the absence of an anisotropic energy gap between exciton states and remains unchanged in the presence of exciton–phonon coupling. However, for finite anisotropic, energy gap concurrence decreases with increasing temperature of the phonon bath.We discuss generation of two types of entangled states of two photons: noon state, which is entangled in number and polarization, and polarization-entangled state, which is entangled in polarization and frequency. We consider a single quantum dot coupled with a bimodal cavity in a strong coupling regime. We analyze the effect of exciton–phonon coupling on concurrence of the generated entangled states. We find that for both states, concurrence is maximum in the absence of an anisotropic energy gap between exciton states and remains unchanged in the presence of exciton–phonon coupling. However, for finite anisotropic, energy gap concurrence decreases with increasing temperature of the phonon bath.

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In the first part of this thesis, by using the two-photon Jaynes - Cummings Model (JCM),\nwe show how NOON states may be generated entangling two cavities, by passing atoms\nthrough them. The atoms interact with each cavity via two-photon resonant transitions.\nWe take advantage of the fact that depending on the state the atom enters (excited or\nground), it leaves or takes two photons per interaction and leaves the cavities in a pure\nstate.\nIn the second part of this thesis, we consider the Hamiltonian of a single ion vibrating in\ntwo dimensions interacting with a laser, we show how NOON states may be generated in\nion traps. We use the individual interaction of light with each of two vibrational modes of\nthe ion to entangle them. This allows us to generate NOON states with N = 8.In the first part of this thesis, by using the two-photon Jaynes - Cummings Model (JCM),\nwe show how NOON states may be generated entangling two cavities, by passing atoms\nthrough them. The atoms interact with each cavity via two-photon resonant transitions.\nWe take advantage of the fact that depending on the state the atom enters (excited or\nground), it leaves or takes two photons per interaction and leaves the cavities in a pure\nstate.\nIn the second part of this thesis, we consider the Hamiltonian of a single ion vibrating in\ntwo dimensions interacting with a laser, we show how NOON states may be generated in\nion traps. We use the individual interaction of light with each of two vibrational modes of\nthe ion to entangle them. This allows us to generate NOON states with N = 8.

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Entangled photons from a strongly coupled quantum dot-cavity system

R. Johne, Николай Алексеевич Гиппиус, G. Malpuech

A quantum dot strongly coupled to a photonic crystal has been recently proposed as a source of entangled photon pairs [R. Johne et al., Phys. Rev. Lett. 100, 240404 (2008)]. The biexction decay via intermediate polariton states can be used to overcome the natural splitting between the exciton states coupled to the horizontally and vertically polarized light modes so that high degrees of entanglement can be expected. We investigate theoretically the features of realistic dot-cavity systems, including the effect of the different oscillator strength of excitons resonances coupled to the different polarizations of light. We show that in this case, an independent adjustment of the cavity resonances is needed in order to keep a high entanglement degree. We also consider the case when the biexciton-exciton transition is also strongly coupled to a cavity mode. We show that a very fast emission rate can be achieved allowing the repetition rates close to the terahertz range. Such fast emission should however be paid for by a very complex tuning of the many strongly coupled resonances involved and by a loss of quantum efficiency. Altogether a strongly coupled dot-cavity system seems to be very promising as a source of entangled photon pairs.A quantum dot strongly coupled to a photonic crystal has been recently proposed as a source of entangled photon pairs [R. Johne et al., Phys. Rev. Lett. 100, 240404 (2008)]. The biexction decay via intermediate polariton states can be used to overcome the natural splitting between the exciton states coupled to the horizontally and vertically polarized light modes so that high degrees of entanglement can be expected. We investigate theoretically the features of realistic dot-cavity systems, including the effect of the different oscillator strength of excitons resonances coupled to the different polarizations of light. We show that in this case, an independent adjustment of the cavity resonances is needed in order to keep a high entanglement degree. We also consider the case when the biexciton-exciton transition is also strongly coupled to a cavity mode. We show that a very fast emission rate can be achieved allowing the repetition rates close to the terahertz range. Such fast emission should however be paid for by a very complex tuning of the many strongly coupled resonances involved and by a loss of quantum efficiency. Altogether a strongly coupled dot-cavity system seems to be very promising as a source of entangled photon pairs.

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Effective protocol for generating NOON states of resonator modes

Yi‐Hao Kang, Zhe-Ping Lin, Jianqun Yang +4 more

We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.

Optics ExpressNov 23, 20234 citations

Publisher's Note: Method for generating a photonic NOON state with quantum dots in coupled nanocavities [Phys. Rev. A 96 , 013853 (2017)]

Kenji Kamide, Yasutomo Ota, Satoshi Iwamoto +1 more

Physical Review AAug 7, 20171 citation

Generating double NOON states of photons in circuit QED

Qi-Ping Su, Hui-Hao Zhu, Li Zhi Yu +4 more

To generate a NOON state with a large photon number $N$ , the number of operational steps could be large and the fidelity will decrease rapidly with $N$ . Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only $N+2$ operational steps. One application of double NOON states is to get a phase error of $1/(2N)$ in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least $2N$ operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only $N+2$ operational steps. One application of double NOON states is to get a phase error of $1/(2N)$ in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least $2N$ operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.

arXiv:1702.02678Physical Review AFeb 27, 201727 citations

N=2

), can be extended toward a higher NOON state (

N>2

) based on our recipe, which is applied to the case of

N=4

as an example.

To generate a NOON state with a large photon number

N

, the number of operational steps could be large and the fidelity will decrease rapidly with

N

. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only

N+2

operational steps. One application of double NOON states is to get a phase error of

1/(2N)

in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least

2N

operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.