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arXiv:2006.04498

Collective Photon Assisted Dressing of Atomic Levels by the number $N$ of Correlated Atoms

R. Shuker, Gennady A. Koganov

Published Jun 8, 2020• 0 citations
arXivHTMLPDF

Abstract

Enhancement of the sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices requires introducing new physical processes to improve on their present achievements. Many body collective correlations among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As these correlations introduce interference terms in the intensity of the scattering amplitudes, they may enhance the signal as $N(N-1)$ for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of $N^2$ and contribute to better sensitivity in quantum metrology. Moreover atomic correlation may provide quantum noise limit, Heisenberg limit. In the present communication excitation exchange induced by photons in a cavity between two atoms is calculated and clearly exhibits correlation and collective effects. A novel operator is introduced that expresses photon-induced excitation exchange that takes in account energy conservation, $V_{ij}=\hat{a}^\dagσ_iσ_j^†\hat{a}$, $σ_i=\left|g\right\rangle_{i}\left\langle e\right|_{i}$ is lowering operator of $i$-th atom, and $\hat{a}^†,\hat{a}$ are photon creation and annihilation operators. Here $i$ and $j$ stand for two atoms. This operator describes real or virtual photon assisted dipole-dipole interaction. Moreover, it conserves the total number of excitations in the joint em field and the quantum system. Experimental challenges are suggested.

DOI
10.48550/arxiv.2006.04498

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Abstract The sensitivities of optical magnetometers, atomic clocks and atom interferometers and other quantum metrology devices, whose signals are linear in the number N of active atoms, have practically arrived at their theoretical limit. Further enhancement of the sensitivities of such devices requires the introduction of new physical processes to improve on their present achievements. Many-body collective correlation among the atoms, spins or, in general, quantum systems may prove to be a suitable method. As such correlations introduce interference terms in the intensity of the scattering amplitudes they may enhance the signal as N ( N − 1) for N correlated quantum systems. These correlations enhance the signal to noise ratio by a factor of N 2 and contribute to better sensitivity in quantum metrology. Moreover, atomic correlation may provide a quantum noise limit, the Heisenberg limit. In the present letter a novel operator is introduced that expresses photon-induced excitation exchange that takes into account energy conservation, V i j = a ˆ † σ i σ j † a ˆ , where σ i = g i e i is the lowering operator of the i - th atom, and a ˆ † , a ˆ are photon creation and annihilation operators. Here i and j stand for two different atoms. This operator describes real or virtual photon-assisted excitation exchange between two atoms. Moreover, it conserves the total number of excitations in the joint electromagnetic field and the quantum system. A photon-induced excitation exchange between two atoms is calculated and clearly exhibits correlation and collective effects.
Microscopic models based on multilevel atoms are central to optimizing nonlinear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work, we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of interatomic correlations and collective decay over the photons created in this nonlinear process is then explored. We identify three regions of operation: (i) laser-dominated, (ii) intermediate, and (iii) dipole-dominated. The dependence of single- and two-photon correlations is studied in detail for each region by varying atomic orientations and laser parameters consistent with current experiments involving atomic gases. Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning—with general features that can be obtained in an isolated atom scheme—to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photon correlations. Signatures of these processes are identified for existing experimental realizations. The intuition obtained from this connection helps to uncover relevant parameters that could be exploited for quantum control protocols based on dispersive and dissipative cooperative effects in multilevel systems.
Many quantum device signals are proportional to the number of the participating atoms that take part in the detection devices. Among these are optical magnetometers, atomic clocks, quantum communications and atom interferometers. One way to enhance the signal-to-noise ratio is to introduce atom entanglement that increases the signal in a super-radiant-like effect. A coherent em field inside a laser cavity is suggested to achieve atoms’ correlation/entanglement. This may also play an important role in the basic quantum arena of many-body physics. An initial novel experiment to test the realization of atoms’ correlation is described here. A Cs optical magnetometer is used as a tool to test the operation of a cell-in-cavity laser and its characteristics. A vapor cell is inserted into an elongated external cavity of the pump laser in Littrow configuration. Higher atom polarization and reduced laser linewidth are obtained leading to better magnetometer sensitivity and signal-to-noise ratio. The Larmor frequency changes of the Free Induction Decay of optically pumped Cs atomic polarization in the ambient earth magnetic field at room temperature is measured. Temporal changes in the magnetic field of less than 10 pT/√Hz are measured. The first-order dependence of the magnetic field on temperature and temperature gradients is eliminated, important in many practical applications. Single and gradiometric magnetometer configurations are presented.
In recent years, the study of quantum electrodynamics (QED) in light-matter interactions has discovered various interesting phenomenons that orient many applications. However, due to the ambient entanglement among photons and atoms, few-particle dynamics remains challenging to analyze precisely and limits the progress in several fields. In few-particle systems, different number of atoms interacting with the light field generates drastically different results, even when there is only a single photon involved in the system. The interference between individual atom’s spontaneous emission wavefunctions can cooperatively alter the effective atom-light coupling strength. Depending on the spatial distance between individual of atoms and the involved cavities in the interaction progresses, the collective spontaneous emission rate can alter drastically from superradiance, where the emission rate is enhanced to a high value proportional to the atom number, to subradiance, where the excited atom ensemble stays in a dark state with the light trapped forever. Superradiance provides a promising mechanism to create an ultra-strong light-matter coupling environment, which is an important ingredient for the design of ultra-fast optical devices, frequency comb generation and quantum mirrors. The dark state of subradiance, on the other hand, is essential for the quantum memory implementation. Also, nontrivial phenomenons also occur when multiple photons interacting with a single atom simultaneously. When a finite number of photons incidents on an atom, their scattering through an atom is highly nonlinear, and one special eigenstate component of such nonlinear process, namely photonic bound states, exhibits many interesting properties in nonlinear quantum optical systems. The photons in such state are strongly bunched with each other, as if a virtual attractive force is in effect. Also, the frequency of photons are anti-correlated so that their total frequency remains a constant value, no matter how arbitrary the frequency of any individual is. Thesefeatures benefit certain nonlinear quantum processes for quantum computing and quantum imaging. Specially for two-photon excitation imaging, the same-parity two-level fluorophore molecules suffers from extremely low excitation efficiencies due to the far off-resonant intermediate states. However, by replacing the current commonly used ultrashort laser pulse illuminations with two photon bound state photon pairs, namely photonic dimers, the efficiency can be enhanced to orders of magnitude higher. Such exceptionally high excitation efficiency can potentially bring the current in vivo deep brain imaging depth from millimeter level to several centimeters. To obtain a stable source of such photonic dimers, it is found that a laser structure with gain medium of two-photon emission materials is capable of generating the coherent state of photonic dimer and can serve as a promising light source for nonlinear quantum optical devices.
Paradigmatic spin Hamiltonians in condensed matter and quantum sensing typically utilize pair-wise or 2-body interactions between constituents in the material or ensemble. However, there is growing interest in exploring more general nnn-body interactions for n>2n >2n>2, with examples including more efficient quantum gates or the realization of exotic many-body fracton states. Here we realize an effective n=3n=3n=3-body Hamiltonian interaction using an ensemble of laser-cooled atoms in a high finesse optical cavity with the pseudo-spin 1/2 encoded by two atomic momentum states. To realize this interaction, we apply two dressing tones that coax the atoms to exchange photons via the cavity to realize a virtual 6-photon process, while the lower-order interactions destructively interfere. The resulting photon mediated interactions are not only n>2n>2n>2-body but also all-to-all(-to-all) and therefore of great interest for fast entanglement generation and quantum simulation of exotic phases such as the long sought but not yet observed charge-Qe superconductors, with Q=2nQ=2nQ=2n . The versatility of our experimental system can also allow for extending to 3-body interactions in multi-level systems or to higher-order interactions, such as the signature of a n=4n=4n=4-body interaction mediated by a virtual eight photon process that we also observe.
We study a system of N two-level atoms interacting with a coherent field a resonant cavity in a self-consistent manner. No direct correlation between the atoms, such as induced by dipole–dipole interaction, is included. Initially all atoms are not exited, and there are n0 photons in the cavity. We show that the system reveals collective-like behavior, which stems from mutual influence of the atoms and coherent field in the cavity. In distinction from conventional dressing of atomic states by strong electromagnetic field, the system of N two-level atoms in a resonant cavity is actually dressed by both the number of photons and the number of atoms N. This double dressing results in both N and n0-dependent oscillation frequency, ω(n0,N). At N>>n0 the spectral density contains, apart from the main peak at the collective atomic frequency gN, additional features at odd sub-harmonics. There is interference signature at the double dressing spectrum which has half-peaks and half-dips that is a synchronization among the frequencies of photon and the atomic dressings. It is a beautiful manifestation of quantum interference in the present novel double dressing by the number n of photons and by the number N of atoms.