JP3682266B2 - Single photon generator - Google Patents

Description

【００２８】
ただし、ここでは、基底ベクトルを媒質とコヒーレント光および共鳴モードの間に相互作用のない状態｛｜ｕ，０＞，｜ｅ，０＞，｜ｇ，１＞｝にとり、共鳴モードの真空共鳴ラビ周波数を２ｇ、コヒーレント光の共鳴ラビ周波数をΩ_Tとした。このハミルトニアンの三つの固有状態は、それぞれ下記（２）式で表すことができる。
【００２９】
【数２】

【００３０】
ここで、（２）式中のΘとΦは、それぞれ下記（３）式の条件を満たす角である。
【００３１】
【数３】

【００３２】
コヒーレント光を照射する直前の系の固有状態の一つ｜ａ⁰＞は、Ω_T＝０であることから、系の初期状態｜ｕ，０＞と等しい。また、コヒーレント光照射後の系の固有状態の一つ｜ａ⁰＞は、もし、Ω_T≫２ｇであるならば、状態｜ｇ，１＞に等しいことがわかる。
【００３３】
したがって、コヒーレント光を照射する場合に、Ω_Tを断熱的に変化させることができれば、つまりコヒーレント光の強度を「ゆっくり」増加させることができれば、この系の状態は状態｜ｅ，０＞を含んだ固有状態｜ａ⁺＞および｜ａ^-＞が混ざることなく、固有状態｜ａ⁰＞を保ったままコヒーレント光の強度に応じて状態｜ｕ，０＞から状態｜ｇ，１＞に遷移する。ここで「ゆっくり」とは、Ω_Tが変化する時間スケールをΔτとすると、この時間スケールが媒質と共鳴モードとの間の相互作用の時間スケールであるラビ周波数２ｇの逆数に対して十分長いことを示し、Δτ≫１／２ｇと表すことができる。したがって、このような条件を満たすコヒーレント光パルスによって、媒質を第一の準位から第三の準位への実励起を伴わずに第一の準位から第二の準位へ遷移させることができ、光共振器の共鳴モードに一つの光子が生成される。上述したコヒーレント光の強度変化を図２（ｂ）に、状態｜ｕ，０＞から状態｜ｇ，１＞への遷移を図２（ｃ）に示す。
【００３４】
以上で説明したアディアバティック・パッセージの手法において、特に第三の準位（｜ｅ，０＞）への実励起を避けている理由は、この準位からの自然放出によって光子エネルギーが失われ、光子発生確率が低下するのを防ぐためである。ただし、共鳴モードの真空共鳴ラビ周波数２ｇ、およびこの共鳴モードの減衰レート（減衰時間の逆数）２κ₁が、それぞれ、第三の準位の自然放出レート２γに比べて十分大きい場合、つまり２ｇ，２κ₁≫２γを満たす場合には、自然放出で失われるよりも十分早く共振器から光子を取り出すことができるため、アディアバティック・パッセージの手法を用いず、第三の準位への実励起が伴ってもかまわない。この場合には、コヒーレント光パルスを「ゆっくり」立ち上げる必要がないため、アディアバティック・パッセージの方法を用いる場合よりも高速に単一光子を発生することができる。
【００３５】
このようにして光共振器の共鳴モードに生成された単一光子は、上で述べたように、媒質の第二の準位と第三の準位との間の遷移に結合し、かつ発生させるべき単一光子の周波数に対応する共鳴周波数の共鳴モードを有する光共振器を通じて、本発明の実施形態に係る単一光子発生素子から外部へと放出され、光共振器内に光子は存在しなくなる。つまり、前記の記号を用いて書き表せば、媒質−光共振器結合系の状態は｜ｇ，０＞へ遷移する。
【００３６】
以上で説明した過程を繰り返し行うことによって、任意の単一光子パルス列を生成するためには、媒質−光共振器結合系を状態｜ｇ，０＞から状態｜ｕ，０＞に遷移させ、初期状態に戻す必要がある。本発明の特徴はこの初期状態への状態の復元手段にある。本発明の実施形態に係る単一光子発生素子は、この状態復元のために、媒質の第一の準位と第二の準位との間の遷移に結合する共鳴周波数の共鳴モードを用いる。この共鳴モードは、たとえば上述した光共振器（媒質の第二の準位と第三の準位との間の遷移に結合し、かつ発生させるべき単一光子の周波数に対応する共鳴周波数の共鳴モードを有する）とは別の共振器、例えばマイクロ波共振器を用いて用意することができる。また、この共鳴モードは、第一の準位と第二の準位との間の遷移周波数が第二の準位と第三の準位との間の遷移周波数と同程度である場合には、上述した光共振器を兼用して、その異なる共鳴モードを用いることもできる。
【００３７】
図３を参照して、媒質−共振器結合系を初期状態へ復元する手法を説明する。以下の説明においては、二つの共鳴モードの区別を容易にするために、媒質の第二の準位と第三の準位との間の遷移に結合し、かつ発生させるべき単一光子の周波数に対応する共鳴周波数の共鳴モードを共鳴モード１と呼び、媒質の第一の準位と第二の準位との間の遷移に結合する共鳴周波数の共鳴モードを共鳴モード２と呼ぶ。ここで、共鳴モード１に存在する光子数を｜ｎ₁＞で表し、共鳴モード２に存在する光子数を｜ｎ₂＞と表すと、媒質および二つの共鳴モードの状態を合わせて、例えば｜ｇ，ｎ₁，ｎ₂＞と書き表すことができる。つまり、系の状態を表すこの記号において、一番左の記号は媒質の準位を表し、二番目の数は共鳴モード１の光子数を表し、三番目の数は共鳴モード２の光子数を表す。例えば単一光子を発生させた直後の系の状態は｜ｇ，０，０＞であり、復元すべき系の初期状態は｜ｕ，０，０＞である。
【００３８】
共鳴モード２は状態｜ｇ＞と状態｜ｕ＞の遷移に結合し、状態｜ｇ，０，０＞と状態｜ｕ，０，１＞の間、および、状態｜ｇ，１，０＞と状態｜ｕ，１，１＞の間のラビ振動を誘起する。このとき、共鳴モード２が誘起するラビ振動の真空共鳴ラビ周波数２ｇ₂が、共鳴モード１の減衰レート２κ₁に比べて十分小さい、つまりκ₁≫ｇ₂である場合を考える。この条件が満たされれば、状態｜ｇ，１，０＞に対しては、共鳴モード１からの光子の減衰による状態｜ｇ，０，０＞への遷移が、共鳴モード２によって誘起されるラビ振動による状態｜ｕ，１，１＞への遷移よりも支配的である。したがって、系は状態｜ｇ，１，０＞から単一光子発生に伴って速やかに状態｜ｇ，０，０＞に遷移する。
【００３９】
系はその後、共鳴モード２によって誘起されるラビ振動によって状態｜ｇ，０，０＞と状態｜ｕ，０，１＞の間を振動する。このラビ振動に伴って共鳴モード２に発生した光子は、共鳴モード２が有限な減衰レート２κ₂を有していれば、その減衰レート程度の早さで共振器外部へと放出され、系の状態は｜ｕ，０，０＞へと遷移し、したがって初期状態が復元される。
【００４０】
共鳴モード２、つまり媒質の第一の準位と第二の準位との間の遷移に結合する共鳴周波数の共鳴モードは、結合の強度または共鳴モード自身の特性が可変になっていてもよい。これを実現するためには、共振器（または光共振器）に作用して、その共鳴モードと媒質との間の位置関係または共鳴モードの幾何学形状を変化させる手段を設けることが好ましい。具体的には、ピエゾ素子などを設けて光共振器を変位させるかまたは応力により変形させてもよいし、電熱線やペルチェ素子などを設けて光共振器の温度を制御してもよい。単一光子発生素子において任意の単一光子パルス列を発生させる場合には、実用上、高速であればあるほど、つまりパルス列発生の繰り返し周波数が高いほど、有用であることは明白である。この繰り返し周波数を上げるためには、上述したように共鳴モード２と媒質との結合強度や共鳴モード自身の特性が可変になっていることが好ましい。以下にその理由を説明する。
【００４１】
本発明の実施形態に係る単一光子発生素子において、パルス列発生の繰り返し周波数の上限を決めるのは、単一光子発生後に状態を復元するためにかかる時間である。この時間は共鳴モード２の誘起するラビ振動の真空共鳴ラビ周波数２ｇ₂および共鳴モード２の減衰レート２κ₂によって決定される。共鳴モードの真空共鳴ラビ周波数は、主にその共鳴モードの占有する空間の体積（共鳴モード体積）によって決まり、この体積が小さいほど真空共鳴ラビ周波数が大きくなる。また、共鳴モードの減衰レートは、共振器に内在する様々な損失要因（共振器損失）によって決まり、この損失が小さいほど減衰レートも小さくなる。共鳴モード体積と共振器損失とは、それぞれ独立に決められるパラメータであるから、真空共鳴ラビ周波数と減衰レートもそれぞれ独立に決定することができる。
【００４２】
ここで、共鳴モード２の真空共鳴ラビ周波数２ｇ₂および減衰レート２κ₂は、第二の準位の自然放出レートを２γ₂として、共鳴モード２が媒質の第一の準位と第二の準位との間のラビ振動を誘起するのに必要な強結合条件ｇ₂＞κ₂，γ₂を満たさなければならない。また、状態復元のために共鳴モード２を用いることが有用であるためには、第二の準位の自然放出レートよりも共鳴モード２による状態復元のレートが早くなければならないので、ｇ₂，κ₂＞γ₂である。この二つの条件をまとめて書けば、ｇ₂＞κ₂＞γ₂となる。したがって、単一光子パルス列発生の繰り返し周波数の上限はκ₂によって決まることがわかる。繰り返し周波数を上げるためにκ₂を大きくするには、前記の条件を満たすようにｇ₂も大きくしなければならない。しかし、上述した通り、条件κ₁≫ｇ₂があるために、ｇ₂の値をこの条件を超えて大きくすることはできず、繰り返し周波数を上げることは困難である。
【００４３】
一方、共鳴モード２と媒質との結合強度や共鳴モード自身の特性が可変であれば、状況に応じてｇ₂の値を上記の条件を超えて大きくとることができ、繰り返し周波数を上げることができる。例えば、単一光子発生前に系が状態｜ｇ，１，０＞にいる間は、ｇ₂の値が条件κ₁≫ｇ₂を満たすのに十分な程度小さくしておき、状態｜ｕ，１，１＞への不要な遷移を抑制する。単一光子発生後に系が状態｜ｇ，０，０＞に遷移した後は、ｇ₂が大きな値をとるように共鳴モード２と媒質との結合強度や共鳴モード自身の特性を変化させ、系を素早く初期状態｜ｕ，０，０＞へと復元させる。こうして、単一光子パルス列発生の繰り返し周波数を上げることが可能である。このような状態復元を実現するには、コヒーレント光によるπパルス照射と同じように系の制御を必要とする。しかし、コヒーレント光によるπパルス照射の場合にはラビ振動に同期した制御が必要であったのに対し、共鳴モード２の変化はそのような同期制御を必要とせず格段に簡便な方法である。
【００４４】
以上において、本発明の実施形態に係る単一光子発生素子の構成要素を順に説明した。以下、理解を助けるために、この単一光子発生素子を用いた単一光子の発生を経時的に説明する。図１（ａ）〜（ｄ）に、本発明の実施形態に係る単一光子発生素子における、単一光子発生に関与する準位を示すとともに単一光子発生のタイミングチャートを示す。
【００４５】
本発明の実施形態に係る単一光子発生素子は、所定の三準位構造を有する媒質を用い、この媒質に二つの共鳴モードを結合し、コヒーレント光を照射することで、単一光子を繰り返し発生させる。図１（ａ）に示すように、発生させるべき単一光子の周波数に対応する共鳴周波数の共鳴モードを共鳴モード１とし、媒質の状態を復元するために用いる共鳴モードを共鳴モード２とする。媒質の準位をエネルギーの低い方から順に｜ｕ＞，｜ｇ＞，｜ｅ＞、共鳴モード１の光子数を｜ｎ₁＞、共鳴モード２の光子数を｜ｎ₂＞とし、二つの共鳴モードに結合した媒質の状態を例えば｜ｕ，ｎ₁，ｎ₂＞と表す。以下、図１（ａ）に記載した状態をより具体的に説明する。
状態｜ｕ，０，０＞は、媒質が第一の準位にあり、共鳴モード１の光子数が０、共鳴モード２の光子数が０である状態を示す。
状態｜ｕ，１，１＞は、媒質が第一の準位にあり、共鳴モード１の光子数が１、共鳴モード２の光子数が１である状態を示す。
状態｜ｕ，０，１＞は、媒質が第一の準位にあり、共鳴モード１の光子数が０、共鳴モード２の光子数が１である状態を示す。
状態｜ｇ，１，０＞は、媒質が第二の準位にあり、共鳴モード１の光子数が１、共鳴モード２の光子数が０である状態を示す。
状態｜ｇ，０，０＞は、媒質が第二の準位にあり、共鳴モード１の光子数が０、共鳴モード２の光子数が０である状態を示す。
状態｜ｅ，０，０＞は、媒質が第三の準位にあり、共鳴モード１の光子数が０、共鳴モード２の光子数が０である状態を示す。
【００４６】
媒質−共振器結合系を初期状態｜ｕ，０，０＞として用意し、この系に対して図１（ｂ）のようなコヒーレント光パルスを照射する。媒質は媒質の第二の準位と第三の準位との間の遷移にラビ振動を誘起できる共鳴周波数の共鳴モード１と結合しているため、共鳴モード１とコヒーレント光の周波数が第一の準位｜ｕ＞と第二の準位｜ｇ＞の間の遷移に対してラマン共鳴条件を満たせば、媒質−共振器結合系は状態｜ｇ，１，０＞へと遷移する。その後、状態｜ｇ，１，０＞にある媒質−共振器結合系は共鳴モード１の減衰時間程度の幅を持つ単一光子パルスを発生し、状態｜ｇ，０，０＞へと遷移する。ここで、状態｜ｇ，１，０＞と状態｜ｕ，１，１＞は、共鳴モード２によってラビ振動を起す可能性が考えられる。しかし、共鳴モード１の減衰は共鳴モード２によるラビ振動よりも十分速いため、この可能性は無視できるほど小さい。その後、媒質は媒質の第一の準位と第二の準位との間の遷移にラビ振動を誘起できる共鳴周波数の共鳴モード２と結合しているため、状態｜ｇ，０，０＞と状態｜ｕ，０，１＞の間でラビ振動を起すが、共鳴モード２からの光子の減衰によって初期状態｜ｕ，０，０＞へと遷移する。図１（ｃ）にこれらの状態変化の過程をまとめて示す。以上の操作を繰り返し行うことによって、任意のタイミングで図１（ｄ）に示すような単一光子のパルスを繰り返し発生させることができ、任意の単一光子パルス列を生成させることができる。
【００４７】
【実施例】
以下、本発明の実施例を、図面を参照しながら説明する。
【００４８】
（実施例１）
図４に本実施例における単一光子発生素子の構成を示す。この単一光子発生素子は、主要な構成部材として、真空装置１１内に設けられたマイクロ波共振器１２と、マイクロ波共振器１２内に設けられた光共振器１３と、光共振器１３内に保持される媒質としての単一原子１４と、単一原子１４にレーザー光パルスを照射するコヒーレント光源としての半導体レーザー１５を有する。
【００４９】
本実施例では、媒質として単一の¹³³Ｃｓ（１３３セシウム原子）を用いる。真空装置１１内でセシウム原子群２４を冷却用レーザービームによって捕獲・冷却して、原子の運動エネルギーを減少させる。この原子群２４を自由落下させ、マイクロ波共振器１２の上面に設けられた孔を通して光共振器１３内に導入する。このとき、原子群２４に対してレーザー冷却を施す時間を調整することで捕獲する原子の数を増減させ、光共振器内に導入する原子の数を制御することができる。本実施例では、冷却時間を０．１秒程度に設定することにより単一の原子を導入している。
【００５０】
光共振器１３内に導入された単一原子１４を、原子の共鳴周波数に対して遠共鳴にチューンされた一対の光ポテンシャル形成用レーザービームによって、光共振器１３内に静止させる。このレーザービームによって形成される光ポテンシャル形状は、単一原子１４の静止位置が光共振器１３の幾何学的中心付近となるように制御されている。
【００５１】
光共振器１３は一対の誘電体多層膜反射鏡を対向させたファブリ−ペロー型の構成になっている。一方の反射鏡の後端にはピエゾ素子２３が取り付けられている。このピエゾ素子２３への印加電圧によって光共振器１３の長さを制御でき、共鳴周波数を変化させることができる。また、一対の反射鏡のうち一方は他方に比べて反射率が高く設計されており、光共振器１３内に発生した光子を特定の一方向に選択的に放出できるようになっている。
【００５２】
光共振器１３の周囲には、ニオブ製のマイクロ波共振器１２が構築されている。このマイクロ波共振器１２は立方体形状をしており、ＴＥ₀₁₁モードで共振する。また、マイクロ波共振器１２の一つの面にはピエゾ素子２２が取り付けられている。このピエゾ素子２２への印加電圧によってマイクロ波共振器１２に加える応力を変化させてマイクロ波共振器１２共振器の幾何学形状を変形させることができ、共振周波数の調整が可能になっている。
【００５３】
さらに、コヒーレント光源としての半導体レーザー１５によって、ファブリ−ペロー型光共振器１３の対称軸に直交する方向から、マイクロ波共振器１２の側面に設けられた孔を通して光共振器１３中に静止した単一原子１４に対してレーザー光パルスが照射される。この半導体レーザー１５は、回折格子を用いた外部共振器構造を有する。半導体レーザー１５の注入電流、動作温度、外部共振器構造を制御することで、レーザー光パルスの発振周波数が制御される。また、この半導体レーザーから出力されるレーザー光は、音響光学素子（図示せず）を通過する。この音響光学素子に印加するラジオ波のパワーを制御することによって、レーザー光パルスの形状が制御される。
【００５４】
図５に、単一光子発生に関与するセシウム原子の準位構造を示す。本実施例において用いられるのは、セシウム原子の超微細構造準位である６Ｓ_1/2；Ｆ＝３、６Ｓ_1/2；Ｆ＝４、および６Ｐ_3/2；Ｆ＝４の三つの準位である。以後、６Ｓ_1/2；Ｆ＝３を状態｜ｕ＞、６Ｓ_1/2；Ｆ＝４を状態｜ｇ＞、６Ｐ_3/2；Ｆ＝４を状態｜ｅ＞と呼ぶ。
【００５５】
光共振器１３は状態｜ｇ＞と状態｜ｅ＞の間の遷移に対して近共鳴となるように共振器長が調整されている。マイクロ波共振器１２は状態｜ｕ＞と状態｜ｇ＞の間の遷移に対して近共鳴となるように幾何学形状が制御されている。また、光共振器１３とマイクロ波共振器１２の各々の遷移に対する真空共鳴ラビ周波数はそれぞれ２０ＭＨｚおよび５ＫＨｚであり、減衰レートはそれぞれ２ＭＨｚおよび３ＫＨｚである。
【００５６】
上記の二つの共振器に結合した単一原子１４に対して、パルス的にレーザー光を照射することにより、単一光子パルス列を生成させ、マイクロ波共振器１２の側面に設けられた孔および真空装置１１の側面に設けられた孔を通して取り出すことができる。図６に、単一光子パルス列の生成過程のタイミングチャートを示す。本実施例において用いたレーザー光パルスは、準位｜ｕ＞と準位｜ｅ＞の間の遷移に近共鳴であり、そのピーク強度における共鳴ラビ周波数は４０ＭＨｚである。また、レーザー光パルスのパルス形状は半値全幅１０マイクロ秒のガウス型であり、パルス照射間隔は５ミリ秒とした。図６のタイミングチャートから、レーザー光パルスの照射に同期して、単一光子パルスが繰り返し発生していることがわかる。
【００５７】
（実施例２）
図７に本実施例における単一光子発生素子の構成を示す。この単一光子発生素子は、マイクロ波共振器を持たず、光ポテンシャル形成用レーザービームの代わりに磁気ポテンシャル形成用コイル１６を設けている点で、実施例１（図４）の単一光子発生素子と異なる。この磁気ポテンシャル形成用コイル１６は、一対のアンチヘルムホルツ配置のコイル、およびこの一対のコイルの対称軸に対して直交する軸を対称軸とするコイルからなる３コイル磁気トラップである。その他の構成は、実施例１の単一光子発生素子と同様である。
【００５８】
また、本実施例では、媒質として単一の⁸⁵Ｒｂ（８５ルビジウム原子）を用いる。実施例１と同様に、真空装置１１内でルビジウム原子群２４を冷却用レーザービームによって捕獲・冷却して、原子の運動エネルギーを減少させる。この原子群２４を自由落下させ、光共振器１３内に導入する。本実施例では、冷却時間を０．０５秒程度に設定することにより単一の原子を導入している。
【００５９】
光共振器１３内に導入された単一原子１４を、磁気ポテンシャル形成用コイル（３コイル磁気トラップ）１６の形成する磁気ポテンシャルによって、光共振器内に静止する。このコイルによって形成される磁気ポテンシャル形状は、単一原子１４の静止位置が光共振器１３の幾何学的中心付近となるように制御されている。
【００６０】
光共振器１３は、実施例１と同様に、一対の誘電体多層膜反射鏡を対向させたファブリ−ペロー型の構成になっており、一方の反射鏡の後端に取り付けられたピエゾ素子２３によって共鳴周波数を変化させることができるとともに、一方の反射鏡は他方に比べて反射率が高く設計されており、光共振器１３内に発生した光子を特定の一方向に選択的に放出できるようになっている。
【００６１】
さらに、コヒーレント光源としての半導体レーザー１５によって、ファブリ−ペロー型光共振器１３の対称軸に直交する方向から、光共振器１３中に静止した単一原子１４に対してレーザー光パルスが照射される。この半導体レーザー１５は回折格子を用いた外部共振器構造を有し、この半導体レーザー１５から出射された種光は半導体光アンプ（図示せず）で増幅される。半導体レーザー１５の注入電流、動作温度、外部共振器構造、および半導体光アンプの駆動電流を制御することで、レーザー光パルスの発振周波数およびパルス形状が制御される。
【００６２】
図８に、単一光子発生に関与するルビジウム原子の準位構造を示す。本実施例において用いられるのは、ルビジウム原子の超微細構造準位である５Ｓ_1/2；Ｆ＝２、５Ｐ_3/2；Ｆ＝３、および５Ｄ_5/2；Ｆ＝４の三つの準位である。以後、５Ｓ_1/2；Ｆ＝２を状態｜ｕ＞、５Ｐ_3/2；Ｆ＝３を状態｜ｇ＞、５Ｄ_5/2；Ｆ＝４を状態｜ｅ＞と呼ぶ。
【００６３】
光共振器１３はそのＴＥＭ₀₀モードが状態｜ｇ＞と状態｜ｅ＞の間の遷移に対して近共鳴、ＴＥＭ₀₂モードが状態｜ｕ＞と状態｜ｇ＞の間の遷移に対して近共鳴となるように共振器長が調整されている。つまり、本実施例では、同じ光共振器の異なる二つの横モードを用いて、単一光子発生と状態復元を行う。また、ＴＭＥ₀₀モードとＴＥＭ₀₂モードの各々の遷移に対する真空共鳴ラビ周波数はそれぞれ４００ＭＨｚおよび２０ＭＨｚであり、減衰レートはそれぞれ１００ＭＨｚおよび１０ＭＨｚである。
【００６４】
上記の二つの共鳴モードに結合した単一原子１４に対して、パルス的にレーザー光を照射することにより、単一光子パルス列を生成させ、真空装置１１の側面に設けられた孔を通して取り出すことができる。図９に、単一光子パルス列の生成過程のタイミングチャートを示す。本実施例において用いたレーザー光パルスは、準位｜ｕ＞と準位｜ｅ＞の間の遷移に対して二光子共鳴する周波数にチューンされ、そのピーク強度における二光子共鳴ラビ周波数は８００ＭＨｚである。また、レーザー光パルスのパルス形状は半値全幅１００ナノ秒のガウス型であり、パルス照射間隔は５００ナノ秒とした。図９のタイミングチャートから、レーザー光パルスの照射に同期して、単一光子パルスが繰り返し発生していることがわかる。
【００６５】
【発明の効果】
以上詳述したように本発明によれば、πパルス生成用のコヒーレント電磁波源を用いることなく、真空状態の共鳴モードと媒質との相互作用によって状態が復元され、一つのコヒーレント光源を用いるだけで、繰り返し単一光子パルスを発生することが可能となる。
【図面の簡単な説明】
【図１】本発明の実施形態に係る単一光子発生素子における、単一光子発生に関与する準位、および単一光子発生のタイミングチャートを示す図。
【図２】アディアバティック・パッセージによる状態遷移の手法を説明する図。
【図３】本発明の実施形態に係る単一光子発生素子における、共振器の共鳴モードを用いて系を初期状態へと復元する手法を説明する図。
【図４】実施例１の単一光子発生素子の構成を示す図。
【図５】実施例１の単一光子発生素子に用いられる媒質の準位構造を示す図。
【図６】実施例１の単一光子発生素子における単一光子パルス列発生のタイミングチャートを示す図。
【図７】実施例２の単一光子発生素子の構成を示す図。
【図８】実施例２の単一光子発生素子に用いられる媒質の準位構造を示す図。
【図９】実施例２の単一光子発生素子における単一光子パルス列発生のタイミングチャートを示す図。
【図１０】従来の単一光子発生素子の動作原理を示す図。
【符号の説明】
１１…真空装置
１２…マイクロ波共振器
２２…ピエゾ素子
１３…光共振器
２３…ピエゾ素子
１４…単一原子
２４…原子群
１５…半導体レーザー
１６…磁気ポテンシャル形成用コイル[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a single photon generating element capable of generating an optical pulse consisting of one photon at an arbitrary time.
[0002]
[Prior art]
In recent years, quantum information processing devices such as quantum communication and quantum computers that perform information processing using quantum mechanical superposition states have been actively studied. In digital information processing devices that are generally used at present, information is represented by a definite bit of 0 or 1 as a basic component. On the other hand, in the quantum information processing device, qubits in which state 0 and state 1 can be determined only probabilistically are used as basic components. As a qubit carrier, photons are considered most promising because of their robustness. However, in order to use a photon as a qubit carrier, it is necessary to determine the frequency and the emission direction with high accuracy at an arbitrary timing and to generate one photon at a high repetition rate.
[0003]
A. Kuhn et al. Proposed the following method using a single atom, an optical resonator strongly coupled to the single atom, and laser light and microwave as a single photon generating element satisfying the above conditions ( Appl. Phys. B69, 373 (1999)). FIG. 10 shows a conceptual diagram of this method. In this method, a single atom is assumed to be a Λ-type three-level atom having two long-lived ground levels | u> and | g> and an excited level | e>. This single atom is placed in an optical resonator having a single resonance mode. The transition between the level | g> and the level | e> is close to the resonance frequency of this resonance mode (ie, induces coherent vibration). On the other hand, the transition between the level | u> and the level | e> is far resonance with respect to the resonance frequency of this resonance mode (that is, it does not induce coherent vibration). Also, | 0> and | 1> in FIG. 10 represent the number of photons present in this resonance mode, and the state emits the photon from the resonance mode and absorbs the photon from the resonance mode. It shows the transition between e> and state | g>.
[0004]
The single atom-optical resonator coupling system described above is prepared in the initial state | u, 0>. In order to generate a single photon, a laser light pulse (trigger pulse) having a near-resonant oscillation frequency at the transition between the level | u, 0> and the level | e, 0> for this system. May be irradiated from a direction perpendicular to the axis of symmetry of the optical resonator. At this time, the rise time of the trigger pulse is slow enough to satisfy the adiabatic condition of the single atom-optical resonator coupled system, and the relationship between the oscillation frequency of the laser beam and the resonant frequency of the optical resonator is the Raman resonance of the atom. If the condition is satisfied, the single atom-optical resonator coupled system adiabatically shifts from the state | u, 0> to the state | g, 1>. In other words, by irradiation with a trigger pulse that satisfies the above conditions, the atomic state can be adiabatically changed from | u> to | g>, and one photon can be generated in the resonance mode of the optical resonator.
[0005]
The single photon generated in the resonance mode stays inside the optical resonator for a time corresponding to the decay time of the resonance mode, and is then emitted to the outside of the optical resonator. That is, the single photon generated in the resonance mode is emitted outside the optical resonator as an optical pulse (single photon pulse) having a time width approximately equal to the decay time (resonance mode lifetime) of the resonance mode. Further, the spectrum width of the single photon pulse is equal to the spectrum width of the resonance mode described above, and the emission direction is limited to the symmetry axis direction of the resonance mode. As described above, a single photon generating element is practically required to generate a single photon by accurately determining a frequency and an emission direction at an arbitrary timing. For that purpose, the single photon pulse time width is narrowed to increase the reliability of single photon generation timing, the spectral width is narrowed to increase the frequency accuracy, and the spatial mode pattern is limited to the emission direction. It is necessary to improve the accuracy. The advantage of this method is that the characteristics of the single photon generation (time width, spectral width, spatial mode pattern, etc.) are mainly determined by the resonant mode characteristics of the optical resonator, thus improving the performance of the optical resonator. Thus, a practically useful single photon generating element can be constructed.
[0006]
As a result of outputting a single photon pulse to the outside of the optical resonator, no photons are present inside the optical resonator. That is, the single atom-optical resonator coupled system loses a photon and transitions to a state of | g, 0>, and the atom does not interact with the resonance mode of the optical resonator and the laser beam. For this reason, the system remains in this state unless an operation that causes another interaction is performed, so that two or more photons are not emitted.
[0007]
Recently, M. Hennrich et al. Described the ultrafine structure level 5S of laser-cooled 85 rubidium atoms._1/2F = 2, 5S_1/2F = 3 and 5P_3/2It has been confirmed that a photon group is generated by using this method for a Λ-type three-level system with F = 3 (Phys. Rev. Lett. 85, 4872 (2000)). Since they introduced multiple atoms instead of a single atom in the optical resonator, they did not directly confirm the generation of a single photon pulse. Has been confirmed to be released.
[0008]
By the way, in order to repeat the single photon pulse generation as described above many times, the final state (the state after the single photon pulse generation) | g, 0> is changed to the initial state | u, 0>. Return and repeat the same operation. In order to restore such a state, it has been proposed to use state transition by microwave irradiation. By continuously irradiating a coherent microwave having an oscillation frequency that resonates with a transition frequency between a state | g, 0> and a state | u, 0>, the system is in a state | g, 0> and a state | vibrates between u, 0>. Therefore, by irradiating the microwave in a pulse manner for a time corresponding to half of this oscillation period (π pulse), the system is completely transitioned from the final state | g, 0> to the initial state | u, 0>. Can be made. In addition, two laser beams having different oscillation frequencies that are Raman-resonated at the transition frequency between the state | g, 0> and the state | u, 0> are also irradiated in a π-pulse manner to restore the same state. It has also been proposed to do.
[0009]
According to the conventional method described above, it is possible to generate a single photon pulse triggered by the laser light pulse by irradiating the laser light pulse to the single atom-optical resonator coupled system. After the generation of a single photon pulse, the state is restored to the initial state by irradiating a coherent electromagnetic wave with an appropriate oscillation frequency, and this process is repeated, so that it can be repeated at any timing. It can be seen that generation of photon pulses (single photon pulse train) is possible.
[0010]
However, in the conventional method, since the state restoration depends on the π pulse irradiation of the coherent electromagnetic wave, the state restoration probability varies depending on the pulse shape such as the peak intensity and the time width of the electromagnetic wave pulse and the oscillation frequency. This is because the period of vibration induced between the final state | g, 0> and the initial state | u, 0> changes depending on the intensity and frequency of the electromagnetic wave. Therefore, in order to reliably restore the state, the shape of the electromagnetic wave pulse and the oscillation frequency must be accurately controlled every time. In order to generate the trigger pulse and the π pulse, two or more types of coherent electromagnetic wave sources having different oscillation wavelengths must be prepared. In addition, in order to generate a single photon pulse train, these plural electromagnetic wave sources must be synchronously controlled at an appropriate timing.
[0011]
[Problems to be solved by the invention]
As described above, in the conventional method, when a single photon pulse is repeatedly generated, a coherent electromagnetic wave source for generating one or a plurality of π pulses must be prepared separately from the coherent electromagnetic wave source for generating a trigger pulse. In addition, there is a problem that the control is difficult and the apparatus configuration is complicated.
[0012]
An object of the present invention is to provide a single photon generating element capable of repeatedly generating a single photon pulse without using a coherent electromagnetic wave source for generating a π pulse.
[0013]
[Means for Solving the Problems]
  The single photon generating element according to one embodiment of the present invention has an energy level structure including energy levels of three or more levels, and the predetermined three energy levels of the energy levels are lower in energy. When the first level, second level, and third level are set in order, photoexcitation from the first level to the third level is possible, and one electron is used for the photoexcitation. Medium in which only is excited; on the transition between the second and third levels of said mediumRabi vibration can be inducedAnd an optical resonator having a resonant mode with a resonant frequency corresponding to the frequency of a single photon to be generated; and an oscillation frequency coupled to a transition between the first level and the third level of the medium A coherent light source having a transition between a first level and a second level of the medium;Rabi vibration can be inducedAnd a resonator having a resonance mode having a resonance frequency.
[0014]
  A single photon generating element according to another aspect of the present invention has an energy level structure including energy levels of three or more levels, and the predetermined three energy levels among the energy levels are low in energy. When the first level, the second level, and the third level are set in this order, photoexcitation from the first level to the third level is possible. A medium in which only electrons are excited; and a transition between the second level and the third level of the medium.Rabi vibration can be inducedAnd a resonance mode at a resonance frequency corresponding to the frequency of a single photon to be generated and a transition between the first level and the second level of the medium.Rabi vibration can be inducedAn optical resonator having a resonant mode of a resonant frequency; and a coherent light source having an oscillation frequency coupled to a transition between a first level and a third level of the medium.
[0015]
  The single-photon generating element described above does not use a coherent electromagnetic wave source for generating a π pulse when restoring the state of the medium to an initial state in order to repeatedly generate a single-photon pulse. On the transition between the level and the second levelRabi vibration can be inducedThe state of the medium can be shifted to the initial state by the interaction between the resonance mode of the resonance frequency and the medium, and a single photon pulse can be repeatedly generated reliably and simply at an arbitrary timing.
[0016]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in more detail.
The single photon generating element according to the embodiment of the present invention has a medium having an energy level structure including energy levels of three levels or more. This means that an electron in the medium can take a quantum state having three or more different energy eigenvalues. In such a medium, three predetermined energy levels are selected and used for single photon generation. In this medium, when the three energy levels are the first level, the second level, and the third level in order from the lowest energy, the first level to the third level. Can be photoexcited, and only one electron is excited for the photoexcitation. This condition is necessary to excite only a single electron into a high energy state and to use a single photon emitted when the electron transitions to a low energy state. If a plurality of electrons are excited for a certain excitation, the number of emitted photons is also a plurality.
[0017]
As a medium capable of photoexciting only a single electron, a single atom can be exemplified. For example, if you prepare only one alkali atom such as sodium, rubidium, cesium, etc. and irradiate this atom with a laser beam of an appropriate wavelength, only one electron that constitutes the outermost shell will be emitted from the ground state. It can be excited to an excited state corresponding to the wavelength of light.
[0018]
The single photon generating element according to the embodiment of the present invention is coupled to the transition between the second level and the third level of the medium as described above, and at the frequency of the single photon to be generated. An optical resonator having a resonance mode with a corresponding resonance frequency is included. By irradiating two levels of a medium with a coherent electromagnetic field in a predetermined propagation mode, the medium may vibrate coherently between the two levels. In this case, the process is repeated in which the medium absorbs photon energy from the propagation mode and transitions to the upper level, and emits photon energy to the propagation mode and transitions to the lower level. This is a phenomenon in which the medium exchanges energy with the propagation mode via photons, and it is called Rabbi vibration in the name of the discoverer. This Rabi vibration can be induced using a resonator in a vacuum state (a state in which no photons are present in the resonance mode) without irradiating the medium with a coherent electromagnetic wave. When a medium having a two-level structure is introduced into a resonator in a vacuum state in an excited state, the medium emits photons with respect to the resonance mode of the resonator and transitions to the ground state. Thereafter, the medium absorbs this photon and changes to the excited state again, and this process is repeated. In other words, the resonance mode of the resonance frequency that is coupled between the predetermined levels of the medium refers to a resonance mode that can induce Rabi oscillation with respect to those levels as described above.
[0019]
The single photon is emitted to the outside of the single photon generating element according to the embodiment of the present invention through this optical resonator. Now, in the process of Rabi oscillation as described above, it is assumed that the medium emits one photon in the resonance mode of the optical resonator, and one photon exists in this resonance mode. At this time, if the single photon can be extracted from the resonance mode to the outside of the optical resonator by any method, this means that a single photon is generated from the single photon generating element according to the embodiment of the present invention. Means that.
[0020]
  In order to extract photons outside the optical resonator, for example, a resonance mode having a finite decay time can be used. Usually, an optical resonator is composed of two or more optical reflectors, but the decay time (resonance mode lifetime) of the resonance mode is mainly determined by the reflection loss of the optical reflector. When a photon is present in the optical resonator, the photon is confined in the optical resonator by the high reflectivity of the optical reflector. In terms of geometric optics, this means that the light beam is reflected between two or more high-reflectance optical reflectors and reciprocates many times, and as a result, stays in the optical resonator for a long time. At this time, if a finite reflection loss exists in the optical reflecting mirror, the light beam gradually leaks out of the resonator by the reflection loss every time it is reflected by the optical reflecting mirror. The same applies to photons in terms of quantum mechanics. The photon existence probability in the resonant mode of the optical resonator decays exponentially in the time of the resonance mode lifetime and oozes out of the resonator. (Hereinafter, it may be referred to as “photon attenuation from the resonance mode”).That is, photons can be extracted outside the resonator in a time that is about the resonance mode lifetime. Furthermore, it means that the single photon generating element according to the embodiment of the present invention can generate a single photon with time accuracy about the resonance mode lifetime.
[0021]
The reflection loss is mainly due to the existence of finite scattering rate and transmittance in the optical reflector. Scattering means that light is reflected in a random direction due to fine irregularities on the reflecting surface of the optical reflector or defects inside the optical reflector. On the other hand, transmission means that light passes through the reflecting mirror and is emitted in a predetermined direction. That is, by using an optical reflector that has a sufficiently high transmittance compared to the scattering rate, photons can be emitted with high probability in a predetermined direction when taking out photons outside the optical resonator.
[0022]
Since the frequency of the photon emitted to the outside of the optical resonator is determined by the resonance frequency of the resonance mode of the optical resonator, the optical resonator having the resonance mode of the resonance frequency corresponding to the frequency of the single photon to be generated Used. Also, the frequency accuracy of a single photon to be generated is equivalent to the spectral width of this resonance mode, but this spectral width is equal to the reciprocal of the resonator lifetime. Therefore, the frequency accuracy and time accuracy of a single photon to be generated are in a trade-off relationship, and it is preferable to determine which one should be prioritized according to the situation and determine the characteristics of the optical resonator.
[0023]
Note that the resonance mode of the resonance frequency corresponding to the frequency of the single photon to be generated and coupled to the transition between the second level and the third level of the medium is the intensity of the coupling or the resonance mode itself. The characteristics may be variable. In order to realize this, it is preferable to provide means for acting on the optical resonator to change the positional relationship between the resonance mode and the medium or the geometric shape of the resonance mode. Specifically, a piezo element or the like may be provided to displace the optical resonator or be deformed by stress, or a heating wire or a Peltier element may be provided to control the temperature of the optical resonator. Such a change in resonance mode characteristics, particularly a change in resonance frequency, is important when changing the frequency of a single photon generated from a single photon generating element according to an embodiment of the present invention. Furthermore, if it is possible to change the strength of the coupling with the medium and the resonance frequency, various parameter values that maximize the probability of single photon generation can be found experimentally by sweeping them. Further, if an optical resonator capable of changing the spatial pattern of the resonance mode is used, the position where the photon is generated can be controlled.
[0024]
A single photon generating element according to an embodiment of the present invention includes a coherent light source having an oscillation frequency that couples to a transition between a first level and a third level of a medium. In the initial state before single photon generation, the medium is in the first level. When generating a single photon, as described above, the medium is coupled with the resonance mode of the optical resonator, and a photon is generated in this resonance mode. Since it is assumed that this resonance mode is coupled to the transition between the second level and the third level of the medium, the medium is at the second level and the photon is equal to the resonance mode. One photon is generated by creating two existing states and extracting the photons to the outside of the optical resonator. In other words, using a coherent light source, the state of the medium is changed from the first level to the second level, and the number of photons in the resonance mode of the optical resonator is changed from 0 to 1. .
[0025]
In order to cause the state change between the medium and the resonance mode of the optical resonator, a technique called adiabatic passage can be used. This method will be described with reference to FIGS. As shown in FIG. 2A, the state corresponding to the first level in the medium is | u>, the state corresponding to the second level is | g>, and the state corresponding to the third level is | E>. Also, the resonance mode states of the optical resonator are expressed as | 0> and | 1> using the number of photons. Therefore, in the initial state before the generation of a single photon, the state of the medium-optical resonator coupled system can be expressed as | u, 0> by combining the state of the medium and the resonance mode. In addition, the medium vibrates between the second and third levels due to Rabi oscillation due to coupling with the resonance mode, and accordingly, the number of photons existing in the resonance mode vibrates between 1 and 0. These two vibrating states can be expressed as | e, 0> and | g, 1>.
[0026]
Consider a case where the above-described coherent light is irradiated to this system. When the oscillation frequency of the coherent light satisfies the Raman resonance condition for the medium-optical resonator coupled system, that is, the detuning with respect to the | u> − | e> transition of the oscillation frequency of the coherent light is the resonance frequency of the resonance mode. If the detuning is the same as the detuning with respect to the | g>-| e> transition, the interaction Hamiltonian H can be expressed by the following equation (1).
[0027]
[Expression 1]

[0028]
However, in this case, the basis vector is set to a state {| u, 0>, | e, 0>, | g, 1>} in which there is no interaction between the medium, the coherent light, and the resonance mode, and the resonance mode vacuum resonance rabbi The frequency is 2g and the resonance Rabi frequency of coherent light is Ω._TIt was. The three eigenstates of the Hamiltonian can be expressed by the following equation (2).
[0029]
[Expression 2]

[0030]
Here, Θ and Φ in the equation (2) are angles that satisfy the condition of the following equation (3).
[0031]
[Equation 3]

[0032]
One of the eigenstates of the system immediately before irradiating coherent light | a⁰> Is Ω_TSince = 0, it is equal to the initial state of the system | u, 0>. One of the eigenstates of the system after irradiation with coherent light | a⁰> If Ω_TIf 2g, it can be seen that it is equal to the state | g, 1>.
[0033]
Therefore, when irradiating coherent light, Ω_TCan be changed adiabatically, that is, if the intensity of the coherent light can be increased "slowly", the state of this system is the eigenstate | a including the state | e, 0>.⁺> And | a^-> Is not mixed, eigenstate | a⁰The state transitions from the state | u, 0> to the state | g, 1> according to the intensity of the coherent light while maintaining>. Here, “slow” means Ω_TIs a time scale at which Δt changes, this time scale is sufficiently long with respect to the reciprocal of the Rabi frequency 2g, which is the time scale of the interaction between the medium and the resonance mode, and expressed as Δτ >> 1 / 2g. be able to. Therefore, a coherent light pulse that satisfies these conditions can cause the medium to transition from the first level to the second level without actual excitation from the first level to the third level. One photon is generated in the resonance mode of the optical resonator. FIG. 2B shows the intensity change of the coherent light described above, and FIG. 2C shows the transition from the state | u, 0> to the state | g, 1>.
[0034]
The reason for avoiding actual excitation to the third level (| e, 0>) in the method of the adiabatic passage described above is that the photon energy is lost due to spontaneous emission from this level, This is to prevent a decrease in the photon generation probability. However, the vacuum resonance Rabi frequency 2g of the resonance mode and the attenuation rate (reciprocal of the attenuation time) 2κ of this resonance mode₁Are sufficiently larger than the spontaneous emission rate 2γ of the third level, that is, 2g, 2κ₁>> When 2γ is satisfied, photons can be extracted from the resonator much faster than they are lost by spontaneous emission, so without using the method of the adiabatic passage, with real excitation to the third level. It doesn't matter. In this case, since it is not necessary to raise the coherent light pulse “slowly”, a single photon can be generated at a higher speed than when the method of the adiabatic passage is used.
[0035]
A single photon generated in the resonant mode of the optical resonator in this way is coupled to and generated by the transition between the second and third levels of the medium, as described above. Through the optical resonator having the resonance mode of the resonance frequency corresponding to the frequency of the single photon to be emitted, the single photon generating element according to the embodiment of the present invention is emitted to the outside, and the photon exists in the optical resonator. Disappear. That is, if written using the above symbols, the state of the medium-optical resonator coupled system transitions to | g, 0>.
[0036]
In order to generate an arbitrary single photon pulse train by repeating the above-described process, the medium-optical resonator coupling system is changed from the state | g, 0> to the state | u, 0> It is necessary to return to the state. The feature of the present invention resides in this state restoring means to the initial state. The single photon generating element according to the embodiment of the present invention uses a resonance mode having a resonance frequency coupled to a transition between the first level and the second level of the medium to restore the state. This resonance mode is for example the optical resonator described above (resonance at the resonance frequency coupled to the transition between the second and third levels of the medium and corresponding to the frequency of the single photon to be generated. It can be prepared using a resonator different from that having a mode, for example, a microwave resonator. This resonance mode is also used when the transition frequency between the first level and the second level is the same as the transition frequency between the second level and the third level. The different resonance modes can also be used in combination with the optical resonator described above.
[0037]
  A method for restoring the medium-resonator coupling system to the initial state will be described with reference to FIG. In the following description, the frequency of a single photon to be coupled to and generated in the transition between the second and third levels of the medium in order to facilitate the distinction between the two resonance modes. The resonance mode of the resonance frequency corresponding to is called the resonance mode 1, and the resonance mode of the resonance frequency coupled to the transition between the first level and the second level of the medium is called the resonance mode 2. Here, the number of photons existing in the resonance mode 1 is expressed by | n₁The number of photons existing in resonance mode 2 is represented by | n₂>, The state of the medium and the two resonance modes are combined, for example, | g, n₁, N₂> Can be written. In other words, in this symbol representing the state of the system, the leftmost symbol is the mediumLevelThe second number represents the number of photons in resonance mode 1, and the third number represents the number of photons in resonance mode 2. For example, the state of the system immediately after generating a single photon is | g, 0, 0>, and the initial state of the system to be restored is | u, 0, 0>.
[0038]
Resonance mode 2 is coupled to the transition of state | g> and state | u>, between state | g, 0,0> and state | u, 0,1>, and state | g, 1,0> Rabi oscillations between states | u, 1,1> are induced. At this time, vacuum resonance Rabi frequency 2g of Rabi vibration induced by resonance mode 2₂Is the decay rate 2κ of resonance mode 1₁Small enough compared to₁≫g₂Consider the case. If this condition is satisfied, for the state | g, 1,0>, the transition to the state | g, 0,0> due to photon attenuation from the resonance mode 1 is induced by the resonance mode 2. It is more dominant than the transition to the state | u, 1,1> due to vibration. Therefore, the system quickly transitions from the state | g, 1,0> to the state | g, 0,0> as a single photon is generated.
[0039]
The system then oscillates between the state | g, 0, 0> and the state | u, 0, 1> by Rabi oscillation induced by resonance mode 2. The photons generated in the resonance mode 2 due to the Rabi vibration have a damping rate 2κ with a finite resonance mode 2.₂, It is emitted to the outside of the resonator as quickly as its attenuation rate, and the system state transitions to | u, 0, 0>, so that the initial state is restored.
[0040]
In the resonance mode 2, that is, the resonance mode of the resonance frequency coupled to the transition between the first level and the second level of the medium, the strength of the coupling or the characteristics of the resonance mode itself may be variable. . In order to realize this, it is preferable to provide means for acting on the resonator (or the optical resonator) to change the positional relationship between the resonance mode and the medium or the geometric shape of the resonance mode. Specifically, a piezo element or the like may be provided to displace the optical resonator or be deformed by stress, or a heating wire or a Peltier element may be provided to control the temperature of the optical resonator. In the case of generating an arbitrary single photon pulse train in a single photon generating element, it is apparent that the higher the speed, that is, the higher the repetition frequency of pulse train generation, the more useful in practice. In order to increase the repetition frequency, it is preferable that the coupling strength between the resonance mode 2 and the medium and the characteristics of the resonance mode itself are variable as described above. The reason will be described below.
[0041]
In the single photon generation element according to the embodiment of the present invention, the upper limit of the repetition frequency of pulse train generation is determined by the time taken to restore the state after single photon generation. This time is the vacuum resonance Rabi frequency 2g of the Rabi vibration induced by the resonance mode 2.₂And resonance mode 2 attenuation rate 2κ₂Determined by. The vacuum resonance Rabi frequency of the resonance mode is mainly determined by the volume of the space occupied by the resonance mode (resonance mode volume). The smaller this volume, the higher the vacuum resonance Rabi frequency. The attenuation rate of the resonance mode is determined by various loss factors (resonator loss) inherent in the resonator, and the attenuation rate decreases as the loss decreases. Since the resonance mode volume and the resonator loss are parameters that are independently determined, the vacuum resonance rabbi frequency and the attenuation rate can also be determined independently.
[0042]
Here, the vacuum resonance Rabi frequency 2g of the resonance mode 2₂And attenuation rate 2κ₂Gives the spontaneous emission rate of the second level to 2γ₂The strong coupling condition g necessary for the resonance mode 2 to induce Rabi oscillation between the first level and the second level of the medium₂> Κ₂, Γ₂Must be met. In order to use the resonance mode 2 for the state restoration, the state restoration rate by the resonance mode 2 must be faster than the spontaneous emission rate of the second level.₂, Κ₂> Γ₂It is. If these two conditions are written together, g₂> Κ₂> Γ₂It becomes. Therefore, the upper limit of the repetition frequency of single photon pulse train generation is κ₂It turns out that it is decided by. Κ to increase the repetition frequency₂Is increased so that the above condition is satisfied.₂Must also be larger. However, as mentioned above, the condition κ₁≫g₂Because there is g₂The value of cannot be increased beyond this condition, and it is difficult to increase the repetition frequency.
[0043]
On the other hand, if the coupling strength between the resonance mode 2 and the medium and the characteristics of the resonance mode itself are variable, depending on the situation, g₂Can be made larger than the above condition, and the repetition frequency can be increased. For example, while the system is in the state | g, 1,0> before the generation of a single photon,₂Is the condition κ₁≫g₂Is made small enough to satisfy the condition to suppress unnecessary transitions to the state | u, 1,1>. After the system transitions to the state | g, 0, 0> after single photon generation, g₂The coupling strength between the resonance mode 2 and the medium and the characteristics of the resonance mode itself are changed so as to take a large value, and the system is quickly restored to the initial state | u, 0, 0>. In this way, it is possible to increase the repetition frequency of single photon pulse train generation. In order to realize such state restoration, it is necessary to control the system as in the case of π pulse irradiation with coherent light. However, in the case of π pulse irradiation with coherent light, control synchronized with Rabi oscillation is required, whereas the change in resonance mode 2 is a much simpler method without requiring such synchronous control.
[0044]
In the above, the component of the single photon generating element which concerns on embodiment of this invention was demonstrated in order. Hereinafter, in order to help understanding, generation of single photons using this single photon generating element will be described over time. FIGS. 1A to 1D show levels involved in single photon generation and a timing chart of single photon generation in the single photon generation element according to the embodiment of the present invention.
[0045]
  The single photon generating element according to the embodiment of the present invention uses a medium having a predetermined three-level structure, couples two resonance modes to the medium, and irradiates coherent light, thereby repeatedly repeating single photons. generate. As shown in FIG. 1A, a resonance mode having a resonance frequency corresponding to the frequency of a single photon to be generated is a resonance mode 1, and a resonance mode used for restoring the medium state is a resonance mode 2. The medium levels are set in order from the lowest energy, | u>, | g>, | e>, and the number of photons in resonance mode 1 is set to | n.₁>, The number of photons in resonance mode 2 | n₂>, And the state of the medium coupled to the two resonance modes is, for example, | u, n₁, N₂>.Hereinafter, the state described in FIG. 1A will be described more specifically.
State | u, 0, 0> indicates a state where the medium is at the first level, the number of photons in resonance mode 1 is 0, and the number of photons in resonance mode 2 is 0.
State | u, 1,1> indicates a state where the medium is at the first level, the number of photons in resonance mode 1 is 1, and the number of photons in resonance mode 2 is 1.
State | u, 0, 1> indicates a state in which the medium is at the first level, the number of photons in resonance mode 1 is 0, and the number of photons in resonance mode 2 is 1.
State | g, 1,0> indicates a state in which the medium is at the second level, the number of photons in resonance mode 1 is 1, and the number of photons in resonance mode 2 is 0.
State | g, 0, 0> indicates a state where the medium is in the second level, the number of photons in resonance mode 1 is 0, and the number of photons in resonance mode 2 is 0.
State | e, 0, 0> indicates a state where the medium is at the third level, the number of photons in resonance mode 1 is 0, and the number of photons in resonance mode 2 is 0.
[0046]
  A medium-resonator coupled system is prepared as an initial state | u, 0, 0>, and this system is irradiated with a coherent light pulse as shown in FIG. MediumResonance frequency that can induce Rabi oscillation at the transition between the second and third levels of the medium.Since it is coupled with resonance mode 1, the frequency of resonance mode 1 and coherent light isFirst level| U> andSecond levelIf the Raman resonance condition is satisfied for the transition between | g>, the medium-resonator coupled system transitions to the state | g, 1,0>. Thereafter, the medium-resonator coupled system in the state | g, 1,0> generates a single photon pulse having a width of about the decay time of the resonance mode 1, and transitions to the state | g, 0,0>. . Here, there is a possibility that the state | g, 1, 0> and the state | u, 1, 1> may cause Rabi vibration by the resonance mode 2. However, since the attenuation in the resonance mode 1 is sufficiently faster than the Rabi oscillation in the resonance mode 2, this possibility is negligibly small. Then the medium isThe resonance frequency at which the Rabi oscillation can be induced at the transition between the first level and the second level of the medium.Since it is coupled to the resonance mode 2, Rabi oscillation occurs between the state | g, 0, 0> and the state | u, 0, 1>, but the initial state | u, Transition to 0,0>. FIG. 1 (c) collectively shows the process of these state changes. By repeatedly performing the above operation, a single photon pulse as shown in FIG. 1D can be repeatedly generated at an arbitrary timing, and an arbitrary single photon pulse train can be generated.
[0047]
【Example】
Embodiments of the present invention will be described below with reference to the drawings.
[0048]
Example 1
FIG. 4 shows the configuration of a single photon generating element in this embodiment. This single photon generating element includes, as main components, a microwave resonator 12 provided in the vacuum device 11, an optical resonator 13 provided in the microwave resonator 12, and an optical resonator 13. And a semiconductor laser 15 as a coherent light source for irradiating the single atom 14 with a laser light pulse.
[0049]
In this embodiment, a single medium is used.¹³³Cs (133 cesium atoms) is used. The cesium atom group 24 is captured and cooled in the vacuum apparatus 11 by a cooling laser beam to reduce the kinetic energy of the atoms. This atomic group 24 is dropped freely and introduced into the optical resonator 13 through a hole provided in the upper surface of the microwave resonator 12. At this time, the number of atoms to be captured can be increased / decreased by adjusting the time for applying laser cooling to the atomic group 24, and the number of atoms introduced into the optical resonator can be controlled. In this embodiment, a single atom is introduced by setting the cooling time to about 0.1 seconds.
[0050]
The single atom 14 introduced into the optical resonator 13 is made stationary in the optical resonator 13 by a pair of optical potential forming laser beams tuned to a far resonance with respect to the resonance frequency of the atoms. The optical potential shape formed by this laser beam is controlled so that the stationary position of the single atom 14 is near the geometric center of the optical resonator 13.
[0051]
The optical resonator 13 has a Fabry-Perot type configuration in which a pair of dielectric multilayer film reflecting mirrors are opposed to each other. A piezo element 23 is attached to the rear end of one of the reflecting mirrors. The length of the optical resonator 13 can be controlled by the voltage applied to the piezo element 23, and the resonance frequency can be changed. In addition, one of the pair of reflecting mirrors is designed to have a higher reflectance than the other, so that photons generated in the optical resonator 13 can be selectively emitted in one specific direction.
[0052]
A niobium microwave resonator 12 is constructed around the optical resonator 13. The microwave resonator 12 has a cubic shape, and TE₀₁₁Resonates in mode. A piezoelectric element 22 is attached to one surface of the microwave resonator 12. The geometrical shape of the microwave resonator 12 resonator can be changed by changing the stress applied to the microwave resonator 12 by the voltage applied to the piezo element 22, and the resonance frequency can be adjusted.
[0053]
Further, the semiconductor laser 15 as a coherent light source is used to stand alone in the optical resonator 13 from the direction perpendicular to the symmetry axis of the Fabry-Perot type optical resonator 13 through a hole provided in the side surface of the microwave resonator 12. One atom 14 is irradiated with a laser light pulse. The semiconductor laser 15 has an external resonator structure using a diffraction grating. By controlling the injection current, operating temperature, and external resonator structure of the semiconductor laser 15, the oscillation frequency of the laser light pulse is controlled. Laser light output from the semiconductor laser passes through an acoustooptic device (not shown). The shape of the laser light pulse is controlled by controlling the power of the radio wave applied to the acoustooptic device.
[0054]
FIG. 5 shows the level structure of the cesium atom involved in single photon generation. In this example, 6S which is a hyperfine structure level of a cesium atom is used._1/2F = 3, 6S_1/2F = 4 and 6P_3/2; Three levels of F = 4. After that, 6S_1/2F = 3 is the state | u>, 6S_1/2F = 4 is the state | g>, 6P_3/2F = 4 is referred to as state | e>.
[0055]
The resonator length of the optical resonator 13 is adjusted so as to be near resonance with respect to the transition between the state | g> and the state | e>. The geometry of the microwave resonator 12 is controlled so as to be near resonance with respect to the transition between the state | u> and the state | g>. The vacuum resonance Rabi frequencies for the transitions of the optical resonator 13 and the microwave resonator 12 are 20 MHz and 5 KHz, respectively, and the attenuation rates are 2 MHz and 3 KHz, respectively.
[0056]
A single photon pulse train is generated by irradiating laser light in a pulsed manner to the single atom 14 coupled to the two resonators described above, and a hole and vacuum provided on the side surface of the microwave resonator 12. It can be taken out through a hole provided on the side of the device 11. FIG. 6 shows a timing chart of the generation process of the single photon pulse train. The laser light pulse used in this example is near resonance at the transition between the level | u> and the level | e>, and the resonance Rabi frequency at the peak intensity is 40 MHz. The pulse shape of the laser light pulse was a Gaussian type with a full width at half maximum of 10 microseconds, and the pulse irradiation interval was 5 milliseconds. It can be seen from the timing chart of FIG. 6 that a single photon pulse is repeatedly generated in synchronization with the irradiation of the laser light pulse.
[0057]
(Example 2)
FIG. 7 shows the configuration of a single photon generating element in this embodiment. This single photon generating element does not have a microwave resonator, and is provided with a magnetic potential forming coil 16 instead of the optical potential forming laser beam. Different from the element. The magnetic potential forming coil 16 is a three-coil magnetic trap comprising a pair of anti-helmholtz-arranged coils and a coil having an axis orthogonal to the symmetry axis of the pair of coils. Other configurations are the same as those of the single photon generating element of the first embodiment.
[0058]
In this embodiment, a single medium is used.⁸⁵Rb (85 rubidium atoms) is used. Similar to the first embodiment, the rubidium atom group 24 is captured and cooled by the cooling laser beam in the vacuum apparatus 11 to reduce the kinetic energy of the atoms. The atomic group 24 is dropped freely and introduced into the optical resonator 13. In this embodiment, a single atom is introduced by setting the cooling time to about 0.05 seconds.
[0059]
The single atom 14 introduced into the optical resonator 13 is stopped in the optical resonator by the magnetic potential formed by the magnetic potential forming coil (three-coil magnetic trap) 16. The shape of the magnetic potential formed by this coil is controlled so that the stationary position of the single atom 14 is near the geometric center of the optical resonator 13.
[0060]
As in the first embodiment, the optical resonator 13 has a Fabry-Perot configuration in which a pair of dielectric multilayer film reflecting mirrors are opposed to each other, and a piezo element 23 attached to the rear end of one reflecting mirror. Can change the resonance frequency, and one reflector is designed to have a higher reflectance than the other, so that photons generated in the optical resonator 13 can be selectively emitted in a specific direction. It has become.
[0061]
Further, a laser beam pulse is applied to a single atom 14 stationary in the optical resonator 13 from a direction perpendicular to the symmetry axis of the Fabry-Perot type optical resonator 13 by a semiconductor laser 15 as a coherent light source. . The semiconductor laser 15 has an external resonator structure using a diffraction grating, and the seed light emitted from the semiconductor laser 15 is amplified by a semiconductor optical amplifier (not shown). By controlling the injection current, operating temperature, external resonator structure, and driving current of the semiconductor optical amplifier of the semiconductor laser 15, the oscillation frequency and pulse shape of the laser light pulse are controlled.
[0062]
FIG. 8 shows the level structure of the rubidium atom involved in single photon generation. In this example, 5S which is the hyperfine structure level of the rubidium atom is used._1/2F = 2, 5P_3/2F = 3 and 5D_5/2; Three levels of F = 4. After that, 5S_1/2; F = 2 state | u>, 5P_3/2; F = 3 in the state | g>, 5D_5/2F = 4 is referred to as state | e>.
[0063]
The optical resonator 13 has its TEM₀₀Near resonance, TEM for mode transition between state | g> and state | e>₀₂The resonator length is adjusted so that the mode becomes near resonance with respect to the transition between the state | u> and the state | g>. That is, in this embodiment, single photon generation and state restoration are performed using two different transverse modes of the same optical resonator. TME₀₀Mode and TEM₀₂The vacuum resonance Rabi frequency for each transition of the mode is 400 MHz and 20 MHz, respectively, and the attenuation rate is 100 MHz and 10 MHz, respectively.
[0064]
A single photon pulse train is generated by irradiating laser light in a pulsed manner to the single atom 14 coupled to the two resonance modes described above, and can be taken out through a hole provided on the side surface of the vacuum device 11. it can. FIG. 9 shows a timing chart of the generation process of the single photon pulse train. The laser light pulse used in this example is tuned to a frequency at which two-photon resonance occurs with respect to the transition between the level | u> and the level | e>, and the two-photon resonance Rabi frequency at the peak intensity is 800 MHz. is there. The pulse shape of the laser light pulse was a Gaussian type with a full width at half maximum of 100 nanoseconds, and the pulse irradiation interval was 500 nanoseconds. From the timing chart of FIG. 9, it can be seen that a single photon pulse is repeatedly generated in synchronization with the irradiation of the laser light pulse.
[0065]
【The invention's effect】
As described above in detail, according to the present invention, without using a coherent electromagnetic wave source for generating a π pulse, the state is restored by the interaction between the resonance mode in the vacuum state and the medium, and only one coherent light source is used. It is possible to generate a single photon pulse repeatedly.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating a level involved in single photon generation and a timing chart of single photon generation in a single photon generation element according to an embodiment of the present invention.
FIG. 2 is a diagram for explaining a state transition method based on an adiabatic passage.
FIG. 3 is a diagram for explaining a method of restoring a system to an initial state using a resonance mode of a resonator in a single photon generation element according to an embodiment of the present invention.
4 is a diagram showing a configuration of a single photon generating element of Example 1. FIG.
5 is a diagram showing a level structure of a medium used in the single photon generating element of Example 1. FIG.
6 is a timing chart of single photon pulse train generation in the single photon generating element of Example 1. FIG.
7 is a diagram showing a configuration of a single photon generating element of Example 2. FIG.
8 is a diagram showing a level structure of a medium used in the single photon generating element of Example 2. FIG.
FIG. 9 is a timing chart of single photon pulse train generation in the single photon generation element of Example 2.
FIG. 10 is a diagram showing an operation principle of a conventional single photon generating element.
[Explanation of symbols]
11 ... Vacuum device
12 ... Microwave resonator
22 ... Piezo element
13: Optical resonator
23 ... Piezo element
14 ... single atom
24 ... Atom group
15 ... Semiconductor laser
16 ... Coil for forming magnetic potential

Claims (5)

It has an energy level structure including energy levels of three or more levels, and the predetermined three energy levels among the energy levels, the first level, the second level in order from the lowest energy, When the third level, it is possible to photoexcitation from the first level to the third level, only a single electron is excited for the optical excitation,
An optical resonator capable of inducing a Rabbi oscillation at a transition between the second level and the third level of the medium and having a resonance mode of a resonance frequency corresponding to the frequency of a single photon to be generated;
A coherent light source having an oscillation frequency coupled to a transition between a first level and a third level of the medium;
A single photon generating element comprising: a resonator having a resonance mode having a resonance frequency capable of inducing Rabi oscillation in a transition between a first level and a second level of the medium. It has an energy level structure including energy levels of three or more levels, and the predetermined three energy levels among the energy levels, the first level, the second level in order from the lowest energy, When the third level, it is possible to photoexcitation from the first level to the third level, only a single electron is excited for the optical excitation,
Rabi oscillation can be induced at the transition between the second level and the third level of the medium, and the resonance mode of the resonance frequency corresponding to the frequency of the single photon to be generated and the first level of the medium An optical resonator having a resonance mode of a resonance frequency capable of inducing a Rabi oscillation at a transition between the level and the second level;
A single photon generating device comprising: a coherent light source having an oscillation frequency coupled to a transition between a first level and a third level of the medium.   The single photon generating element according to claim 1, wherein the medium is a single atom.   The apparatus further comprises means for acting on the optical resonator or the resonator to change a positional relationship between the resonance mode and the medium or a geometric shape of the resonance mode. A single photon generating element as described in 1. 2. The resonator having a resonance mode having a resonance frequency capable of inducing Rabi oscillation at a transition between the first level and the second level of the medium is a microwave resonator. A single photon generating element according to 1.

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