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Photon retention in coherently excited nitrogen ions

Quantum coherence in quantum optics is an essential part of optical information processing and light manipulation. Alkali metal vapors, despite the numerous shortcomings, are traditionally used in quantum optics as a working medium due to convenient near-infrared excitation, strong dipole transitions and long-lived coherence. Here, we proposed and experimentally demonstrated photon retention and subsequent re-emittance with the quantum coherence in a system of coherently excited molecular nitrogen ions (N2+) which are produced using a strong 800 nm femtosecond laser pulse. Such photon retention, facilitated by quantum coherence, keeps releasing directly-unmeasurable coherent photons for tens of picoseconds, but is able to be read-out by a time-delayed femtosecond pulse centered at 1580 nm via two-photon resonant absorption, resulting in a strong radiation at 329.3 nm. We reveal a pivotal role of the excited-state population to transmit such extremely weak re-emitted photons in this system. This new finding unveils the nature of the coherent quantum control in N2+ for the potential platform for optical information storage in the remote atmosphere, and facilitates further exploration of fundamental interactions in the quantum optical platform with strong-field ionized molecules.

For several decades, alkali metal atoms have been serving as a backbone of quantum optical platforms [21][22][23] due to a number of unique properties such as sufficiently long coherence time, the lack of inter-vibrational relaxation, and easy access to laser wavelengths capable of the resonant excitation. Alkali metal dimers, which can be created through heating atoms at a high temperature, are another promising candidate for coherent quantum control [24][25][26][27]. Nevertheless, it would be of great importance to explore alternative solutions involving more abundant elements and molecules which are also less chemically reactant and safe to use. In particular, molecular nitrogen ions (N ), which can easily be produced from atmospheric nitrogen using high-intensity femtosecond pulses, emerge as the intriguing model system for exploring quantum coherence effects from abundant energy levels that exhibit rich electron and molecular dynamics [28][29][30][31][32][33][34]. In such a system, the energy diagram is significantly different from that of an atom, i.e., energy differences between lower electronic states of molecular ions are located in near-ultraviolet, visible and near-infrared spectral regions, making it easy to efficiently manipulate the quantum coherence between multiple states by using commonly available lasers. Electronic, vibrational, and rotational coherences are created in molecular ions when electron instantaneously escapes from nucleus in a strong laser field [29]. However, the quantum coherence in strong-field-ionized molecular ions remains largely unexplored, opening the venue for achieving optical information storage and for exploring coherent quantum control in excited nitrogen ions.
In this paper, we unveil the nature of photon retention in N both theoretically and experimentally. The proposed idea of achieving the photon retention using N quantum optical platform is briefly illustrated in Fig. 1. Three electronic states of N , i.e., Σ , Π and Σ (abbreviated as X, A and B), are considered to construct a three-level system as shown in Fig. 1(b). An intense laser at 800 nm is used to ionize molecular N into N and to pump N into the excited A state. The same laser also generates the quantum coherence between X and A states, which keeps reemitting photons near 800 nm for the timescale of picoseconds. The re-emitting is extremely weak that it is hardly measured directly. Yet, once another laser at 1580 nm is injected after the picosecond delay, we find that it can readout such re-emitted photons by promoting the two-photon resonance, which, in its turn, leads to an experimentally observed strong emission at 329.3 nm. In the same time, the population on B(v=4) level significantly amplifies the contribution of the coherently re-emitted photons, resulting in strong 329.3 nm emission, which persists even tens of picosecond after the initial excitation by the 800 nm laser. This report exhibits important coherent quantum control of photons in N , i.e., photon retention, which is fundamentally different from quantum memory for long lifetime in quantum ensembles, points to potential applications of optical information processing and optical quantum network with ions, and also an exciting perspective for remote atmospheric coherent optical information storage at room temperature.
As shown in Fig. 1, a femtosecond laser at 800 nm excites the quantum coherence .
Under the perturbation theory in the weak excitation limit, we have , where is the peak amplitude of the 800 nm laser field, is the full width at half maximum of the laser field, Γ is the dephasing rate, and (0) is the initial population at the level . Such strong coherence provides the photon retention and keeps emitting photons near 800 nm with the coherence time upto picoseconds, with its intensity being approximately described as s ( ) ∝ . Another laser at 1580 nm with the peak amplitude and the same pulse duration is applied at a delay , and is used to read-out the reemitted photon, which triggers a two-photon absorption (TPA) between levels A and B.
The TPA rate can be estimated as . The ultraviolet (UV) radiation from level B to X is then generated and detected. Since the initial excitation (at 800 nm) prepares very large coherence in N for the photon retention with a relatively long time ∼ 1/Γ after the 800 nm laser is gone, the re-emitted photons from the coherence can be read-out by a delayed 1580 nm laser through the TPA process within the time window defined by ∼ 1/Γ. In the following, we will first demonstrate the experimental results to validate our hypothesis of photon retention and then support the experimental data with more accurate numerical simulations to further explore the effect.
With the basic concept of our proposal in mind, we designed our experiment in the nitrogen gas. A commercial Ti:sapphire laser (Legend Elite-Duo, Coherent, Inc.) was used to pump an optical parametric amplifier (OPA), which delivered femtosecond laser pulses tunable from 1200 nm to 2400 nm. The remaining fundamental radiation centered at 800 nm was used as a pump beam to promote N generation. The polarization directions of two laser beams were parallel to each other, and their relative delay was controlled by a motorized translation stage. Two beams were combined using a dichroic mirror and collinearly focused into 5-mbar nitrogen gas using a plano-convex lens (f  20 cm). The peak intensity at the focus was ~2×10 14 W/cm 2 for the 800-nm, 40-fs laser pulse and ~1×10 13 W/cm 2 for the 1580-nm, 60-fs laser pulse, where two laser fields were assumed to have Gaussian shapes in both space and time. The UV radiation exiting from the gas chamber was collected and focused onto a slit of a spectrometer (Shamrock 303i, Andor) for spectral analysis. A set of appropriate filters were placed before the spectrometer to block the residual laser radiation.  Generation of the 329.3 nm radiation after the temporal separation of two laser pulses indicates that TPA from A(v=4) to B(v=4) was triggered by the re-emitted photons and the delayed-injected 1580 nm laser.
We further studied the UV radiation driven by the 800 nm laser field and the delayinjected laser with other wavelengths. When the laser wavelength was tuned to 1910 nm, two-photon resonance from A(v=4) to B(v=4) was no longer satisfied. In this case, the narrow-bandwidth radiation at 329.3 nm was submerged by the non-resonant FWM signal [see inset of Fig. 3(a)]. Similar to other spectral components of FWM, the radiation at 329.3 nm was only observed within the temporal overlap of two laser fields, as illustrated in Fig. 3(a). The comparison between Fig. 2(c) and Fig. 3(a) clearly demonstrates that the cascaded resonant condition in the three-level N system must be fulfilled to generate the strong 329.3 nm radiation after the temporal separation of two laser fields, which agrees with our predication in Fig. 1. When the wavelength of the delayed laser field was tuned to 2070 nm, we could realize one-photon resonant excitation from X(v=0) to A(v=2) and two-photon resonant excitation from A(v=2) to B(v=2) [see Fig. 2(a)]. Although the cascaded resonant condition similar to the 329.3 nm radiation was fulfilled, the 330.8 nm radiation was only observed around zero delay, as shown in Fig. 3(b). This difference for different transitions was beyond our expectation, and hence detailed simulation was necessary to gain a better fundamental understanding.
We performed numerical simulations using Maxwell-Bloch equations. We considered a one-dimensional pencil-like medium with N modeled by a three-level diagram (i.e., X(v=2), A(v=4), B(v=4)) shown in Fig. 2(a). The two-photon excitation of the ⟷ transition was treated as two excitation processes via two dipole-allowed transitions with a detuned intermediate level I [35]. Using the rotating-wave approximation, the Hamiltonian in the interaction picture reads [1] where ℘ is the dipole moment between the ⟷ transition, 1(2) is the slowly varying envelope amplitude of the 800 (1580) nm electric field, and Δ = − 1 is the detuning between ⟷ transition and the 800 nm laser field. Assuming Δ is much larger than any decoherence rate and thus is negligible, one can use steadystate values = [℘ 1 ( − ) + (℘ ) * ]/(ℏΔ) and = [℘ ( − ) + (℘ 1 ) * ]/(ℏΔ) . Hence, the entire light-matter interaction process including two-photon excitation can be described effectively in the densitymatrix equations [35]: where dephasing rates are Γ = + , Γ = ( + ) + , Γ = + , with being the collisional dephasing rate, and ( ) is the spontaneous decay rate from level ( ). The Maxwell equations for field amplitudes read where = 3 /8 , is the transition wavelength, and is the N density. We simulate the FWM signal s as well as the 1 field followed by a We plot numerical results for evolutions of the 800 nm laser and for the cases of  0 and  1 ps in Fig. 4. Results for different initial population (0) on level are considered. After the original 800 nm laser passes through the medium, the calculated laser field shows a long tail with oscillations. The tail is 7~8 orders of magnitude weaker than the main peak, and the intensity ratio of the main peak and the tail is almost independent of (0), as shown in Fig. 4(a). The tail means that is generated and continuously releases weak emission around 800 nm, which is consistent with the theory that photon retention happens, i.e., photons are stored in the coherence and re-emitted. Such re-emitted weak photons in the medium can then be read-out when the 1580 nm laser field is injected with the time delay. For the case of  1 ps, the coherence between levels and arises due to the two-photon excitation process and reaches a larger amplitude as (0) increases [see Fig. 4(c)].
Although is much smaller at  1 ps than that at  0, it is still possible to generate 329.3 nm radiation through the resonant FWM provided the re-emitted photons near 800 nm keeps interacting with ions.
To give a straightforward comparison with experimental results, we plotted calculated spectra of signal fields and integrals of signal intensities versus delay for different (0) values. Signal field spectra for simultaneous pumping from two fields in Fig.   5(a) show a Fano line shape, while the signal field at  1 ps evolves in a large time scale resulting in a narrow spectral line in Fig. 5(b). In contrast to the case of  0, the 329.3 nm signal at  1 ps grows dramatically as (0) increases. This dependence is also shown in curves of the total signal versus delay. As shown in Fig. 5(c), a larger (0) results in a smaller decrease of the intensity versus the delay. For the case of (0) = 0, the 329.3 nm signal at  1 ps is about 10 orders of magnitude weaker than that at  0. Such a weak signal is impossible to be measured experimentally.
Furthermore, after the initially quick drop, the decay rate of the signal becomes smaller, which is consistent with the experimental result in Fig. 2(c). The simulation results show that B-state population is of vital importance for reading-out the re-emitted photon.
The high initial population on the B(v=4) state actually triggers larger coherence between levels B and A during the two-photon resonance procedure, allowing us to experimentally observe the photon retention effect through the coherence-enhanced radiation at 329.3 nm.
Actually, the B(v=4) level can be efficiently populated through three-photon nearresonant excitation shown in Fig. 2(a), which has been demonstrated in previous simulations [30,32]. To confirm this fact experimentally, we injected a femtosecond seed pulse around 330 nm after the 800 nm laser. Although the seed pulse can cover all transitions B(v=2,3,4)→X(v=0,1,2) with ∆v = 2, it is only amplified at 329.3 nm, as shown in Fig. 3(c), indicating that the B(v=4) level has a higher population than the To conclude, we have demonstrated for the first time the photon retention and optical readout in the quantum optical platform made out of nitrogen ions. Photons near 800 nm are stored and re-emitted from the quantum coherence in N , which are re-emitted and then read-out by applying a delayed 1580 nm laser to induce the UV radiation.
Moreover, large population on the B(v=4) level is produced through the three-photon excitation, which largely enhances the read-out signal. Our work reveals that photons re-emitted by strong excited coherence can be used to perform nonlinear process in ionized nitrogen molecules, which triggers a broad interest for potential applications involving those ions such as remote sensing [29], quantum computation [36], as well as quantum simulations [37], and holds possibility for serving as an important tool targeting towards biological imaging [38] and surface spectroscopy [39,40]. Our pioneering experiment performed in molecular nitrogen with tunnel ionization also opens an important route towards future potential implementation of light storage in remote atmospheric regime.