光缔合产生超冷铯分子中的量子现象研究
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摘要
寻求大量产生基态冷分子或超冷分子的高效、可控的方法是目前国内外原子物理界的一个研究热点。由于分子具有较原子复杂的多的能级结构,研究其中的量子现象无论对量子理论本身还是对实现分子凝聚都有重要的意义。本文通过对光缔合产生超冷铯分子及其光谱特性的分析,首次提出可以用一个有效的四能级模型来描述其合成过程,其中两个上能级由0_g~-(6s+6p_(3/2))双阱中的激发态能级组成,并通过隧穿机制耦合在一起。基于该模型,我们对光缔合产生超冷铯分子中的相关量子现象进行了详细研究。主要内容概括如下:
首先,在平均场近似的框架下,引入受激拉曼绝热转移的光脉冲,结合数值求解微分方程组及解析方法,就铯原子凝聚产生铯分子凝聚的最佳条件进行了详细研究。研究发现:在扩展“双光子”共振(包括双光子过程、平均场修正和两激发分子能级之间的隧穿耦合)条件下,可以找到一个高效率的、稳定的原子分子转换条件。在当前实验所允许的(较小的泵谱光Rabi频率)情况下,提出两种方法来获得高的转换效率。第一,在两激光脉冲的有效Rabi频率相等的条件下,调节两脉冲的失谐差,同时最优化参数延迟系数α和脉冲持续T,可以得到高达87.2%的转换效率。第二,采用非相等的Rabi频率,在给定泵浦场有效Rabi频率和泵浦场失谐,调节dump场的有效Rabi频率,同时最优化参数两激光脉冲失谐差、以及α和T,可以得到80.7%的转换效率。
其次,在弱探测光场条件下,通过解析和数值求解系统满足的主方程,分析系统对探测光的吸收性质。研究发现:当两阱之间的隧穿耦合较强时,预言在这种新的四能级过程中存在一种量子双暗共振现象。如同在三能级系统中一样,该双暗共振现象不仅是冷分子产生的信号,而且也为两激发分子态之间的隧穿耦合机制提供了一个有力证据。同时,指出该双暗共振现象还可通过测量原子态的布居数变化而得到。本文也讨论了在实验条件下,系统的其它参数对探测吸收波谱的影响。
接下来,我们对冷的铯原子—分子系统中探测吸收波谱的线宽进行了分析。研究表明:两阱之间的隧穿耦合强度对吸收波谱中心峰的宽度有很大的影响。通过调节其隧穿耦合强度,可以得到比分子激发态线宽小很多的、亚自然线宽的吸收波谱。当隧穿耦合强度σ_(12)=10γ_(ab)_1时,线宽仅为0.56MHz。这就为获得亚自然线宽波谱提供了一个新的、可控的方法。该研究意味着,可以利用这个四能级过程来获得更窄的线宽,此结果与传统三能级过程中窄线宽的获得相比,有较明显的优势,特别是在强的泵谱光强度和大的失谐条件下,仍然可以得到亚自然线宽的波谱线。
最后,对铯原子—分子凝聚系统中CPT态的动力学不稳定性和Landau不稳定性进行了初步的分析,期望找到不稳定区域的参数范围,这部分工作我们正在进行中。
该研究将有助于发展复杂动力学系统中的量子理论,并对非线性光学、精确波谱测量等具有重要的意义。
To develop one effective method to produce mass of cold molecules, even ground state molecules with high transfer efficiency,is one of the hot points in atomic physics field.Due to its complex energy structure,it is not only interesting to quantum theory,but also to experimentally realize the molecular condensates to investigate the quantum phenomenon in producing ultra-cold molecules.Based on the analysis of experimental realization of the cold Cs_2 molecules through photo-association(PA) and experimental research on the character of the spectrum for Cs_2 molecules,one effective four-level model is proposed to describe this process,wherein the two up-level are consisted of two excited molecular states located in the O_g~-(6s+6p_(3/2)) double wells and coupled by the tunneling mechanism.Starting from this simple model,we foucs on the relative quantum phenomenon in this PA process and the main results are following:
Firstly,in the frame of the standard mean-field approximation and after introducing the two stimulated Raman laser pulses,the optimum conditions for producing Cs_2 molecular condensates from ultra-cold Cs atoms are obtained by the numerical and analytical methods.Our results show that a stable STIRAP method with high conversion efficiency could be realized under the extended "two-photon" resonance condition,including two-photon process,mean-field correction and the tunnelling coupling between two upper excited molecular levels.We proposed two methods to obtain the high conversion efficiency under current experimentally less demanding conditions(relative small effective Rabi frequency for pump laser pulse). One is adjusting the detuning difference between two laser pulses,and simultaneously optimizing the delay coefficientαand pulse duration T for same effective Rabi frequencies with up to 87.2%transfer efficiency. Another one is adopting the unequal effective Rabi frequency to obtain the high conversion efficiency.For given effective Rabi frequency and the detuning of pump laser,adjusting the effective Rabi frequency and the detuning of dump laser with up to 80.7%transfer efficiency.
Secondly,we investigated the properties of the probe absorption spectrum under the weak probe field condition by solving the master equations for density opreators.The double dark resonance is predicted in the absorption spectrum when the tunnelling coupling strength is large enough. The double dark resonance not only reveals the formation of the ultra-cold molecules,but also provides further evidence for the tunnelling as one effective coupling mechanism between the two excited molecular states.On the other hand,this novel effect can also be checked by measuring the population of the atom.The effect of the various experimental conditions on this phenomenon has been discussed.
Then,we theoretically analyzed the linewidth of the probe absorption spectrum in a cold Cs atom-molecule system.We found that the tunnelling coupling between the two excited molecular states could be a new controllable parameter and plays an important role to obtain the sub-natural linewidth of the probe absorption spectrum.For example,when the tunneling couple strength fulfilsσ_(12)=10γ_(ab_1),the linewidth is only about 0.66MHz. Moreover,since the linewidth of interest is dominated by the tunnelling coupling,the sub-natural linewidth spectrum is still obtained even in the case of the large laser intensity and the detuning of the pump field.
Finally,we analyzed the dynamical and Landau instabilities for CPT state in Cs atom-molecule condenstates.We expect to obtain the range of unstatble parameter.This work is in preparing.
These works will be helpful to extend the quantum theories to the complex system,and also be interesting in the field of nonlinear optics and measurement of precision spectroscopy etc.
首先,在平均场近似的框架下,引入受激拉曼绝热转移的光脉冲,结合数值求解微分方程组及解析方法,就铯原子凝聚产生铯分子凝聚的最佳条件进行了详细研究。研究发现:在扩展“双光子”共振(包括双光子过程、平均场修正和两激发分子能级之间的隧穿耦合)条件下,可以找到一个高效率的、稳定的原子分子转换条件。在当前实验所允许的(较小的泵谱光Rabi频率)情况下,提出两种方法来获得高的转换效率。第一,在两激光脉冲的有效Rabi频率相等的条件下,调节两脉冲的失谐差,同时最优化参数延迟系数α和脉冲持续T,可以得到高达87.2%的转换效率。第二,采用非相等的Rabi频率,在给定泵浦场有效Rabi频率和泵浦场失谐,调节dump场的有效Rabi频率,同时最优化参数两激光脉冲失谐差、以及α和T,可以得到80.7%的转换效率。
其次,在弱探测光场条件下,通过解析和数值求解系统满足的主方程,分析系统对探测光的吸收性质。研究发现:当两阱之间的隧穿耦合较强时,预言在这种新的四能级过程中存在一种量子双暗共振现象。如同在三能级系统中一样,该双暗共振现象不仅是冷分子产生的信号,而且也为两激发分子态之间的隧穿耦合机制提供了一个有力证据。同时,指出该双暗共振现象还可通过测量原子态的布居数变化而得到。本文也讨论了在实验条件下,系统的其它参数对探测吸收波谱的影响。
接下来,我们对冷的铯原子—分子系统中探测吸收波谱的线宽进行了分析。研究表明:两阱之间的隧穿耦合强度对吸收波谱中心峰的宽度有很大的影响。通过调节其隧穿耦合强度,可以得到比分子激发态线宽小很多的、亚自然线宽的吸收波谱。当隧穿耦合强度σ_(12)=10γ_(ab)_1时,线宽仅为0.56MHz。这就为获得亚自然线宽波谱提供了一个新的、可控的方法。该研究意味着,可以利用这个四能级过程来获得更窄的线宽,此结果与传统三能级过程中窄线宽的获得相比,有较明显的优势,特别是在强的泵谱光强度和大的失谐条件下,仍然可以得到亚自然线宽的波谱线。
最后,对铯原子—分子凝聚系统中CPT态的动力学不稳定性和Landau不稳定性进行了初步的分析,期望找到不稳定区域的参数范围,这部分工作我们正在进行中。
该研究将有助于发展复杂动力学系统中的量子理论,并对非线性光学、精确波谱测量等具有重要的意义。
To develop one effective method to produce mass of cold molecules, even ground state molecules with high transfer efficiency,is one of the hot points in atomic physics field.Due to its complex energy structure,it is not only interesting to quantum theory,but also to experimentally realize the molecular condensates to investigate the quantum phenomenon in producing ultra-cold molecules.Based on the analysis of experimental realization of the cold Cs_2 molecules through photo-association(PA) and experimental research on the character of the spectrum for Cs_2 molecules,one effective four-level model is proposed to describe this process,wherein the two up-level are consisted of two excited molecular states located in the O_g~-(6s+6p_(3/2)) double wells and coupled by the tunneling mechanism.Starting from this simple model,we foucs on the relative quantum phenomenon in this PA process and the main results are following:
Firstly,in the frame of the standard mean-field approximation and after introducing the two stimulated Raman laser pulses,the optimum conditions for producing Cs_2 molecular condensates from ultra-cold Cs atoms are obtained by the numerical and analytical methods.Our results show that a stable STIRAP method with high conversion efficiency could be realized under the extended "two-photon" resonance condition,including two-photon process,mean-field correction and the tunnelling coupling between two upper excited molecular levels.We proposed two methods to obtain the high conversion efficiency under current experimentally less demanding conditions(relative small effective Rabi frequency for pump laser pulse). One is adjusting the detuning difference between two laser pulses,and simultaneously optimizing the delay coefficientαand pulse duration T for same effective Rabi frequencies with up to 87.2%transfer efficiency. Another one is adopting the unequal effective Rabi frequency to obtain the high conversion efficiency.For given effective Rabi frequency and the detuning of pump laser,adjusting the effective Rabi frequency and the detuning of dump laser with up to 80.7%transfer efficiency.
Secondly,we investigated the properties of the probe absorption spectrum under the weak probe field condition by solving the master equations for density opreators.The double dark resonance is predicted in the absorption spectrum when the tunnelling coupling strength is large enough. The double dark resonance not only reveals the formation of the ultra-cold molecules,but also provides further evidence for the tunnelling as one effective coupling mechanism between the two excited molecular states.On the other hand,this novel effect can also be checked by measuring the population of the atom.The effect of the various experimental conditions on this phenomenon has been discussed.
Then,we theoretically analyzed the linewidth of the probe absorption spectrum in a cold Cs atom-molecule system.We found that the tunnelling coupling between the two excited molecular states could be a new controllable parameter and plays an important role to obtain the sub-natural linewidth of the probe absorption spectrum.For example,when the tunneling couple strength fulfilsσ_(12)=10γ_(ab_1),the linewidth is only about 0.66MHz. Moreover,since the linewidth of interest is dominated by the tunnelling coupling,the sub-natural linewidth spectrum is still obtained even in the case of the large laser intensity and the detuning of the pump field.
Finally,we analyzed the dynamical and Landau instabilities for CPT state in Cs atom-molecule condenstates.We expect to obtain the range of unstatble parameter.This work is in preparing.
These works will be helpful to extend the quantum theories to the complex system,and also be interesting in the field of nonlinear optics and measurement of precision spectroscopy etc.
引文
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